My focus is on a more recent period than what you asked for (17th and 18th century Central Europe), but the everyday lives of common people are quite hard to research there as well, and I don't think that for other times the answer will differ substantially. So, here goes: You basically need a multitude of sources, the more the better. People rarely write up what is common and "normal", paying attention instead to the "abnormal". This is valid for today and was possibly even more so back in the day, and that leaves us historians in danger of mistaking unusual situations for past normalcy. It's a bit like internet reviews like on Amazon or Yelp: People are more likely to leave a review if the product (or hotel, or restaurant...) was either exceptionally good or exceptionally bad, but the vast majority of people for whom the product was working just as intended, or where the pizza was good but literally nothing to write home about won't leave any written traces.

So, what is left? Well, firstly we needn't discard the "abnormal" sources altogether. They can serve as sort of a mirror instead through which we can construct an approximation of everyday life. We can also make use of the fact that what seems normal to one group may seem super weird to another who then might write about that. Two good examples of that are imo 1.) Roman grammarians writing about the supposedly "wrong" and "stunted" speech of the lower classes, compiling huge lists of "wrong" words or grammar mechanics and contrasting them with their idea of "proper speech". Today these writings are amongst our most important sources for the Latin spoken on the streets, which in turn was the variety of Latin that eventually evolved into the Romance languages of today. 2.) A recurring feature of the Early Modern were "fashion decrees" (German Kleiderordnungen), in which the authorities tried to prescribe the clothes, their style and also their colour what people were allowed to wear depending on the social group they belonged to. Many of these decrees had to be published again and again, however, which leads us to believe that their effectiveness was limited and that the sort of fashion they describe for the lower classes might have been quite widespread instead.

This also leads me to another manner of source that is quite important, and that is sources connected to any sort of criminal investigation. A favourite example of that is Emmanuel Le Roy Ladurie's Montaillou, a study based on 14th century court records depicting life in the village of Montaillou where a lot of people were accused of being heretics. The leading investigator (who would later become Pope) was quite adept at his jobs, patiently recording everything the suspects told him in great detail. When you read Le Roy Ladurie's book, at times you feel like the people featuring in it could be standing right next door even though they have been dead for many centuries now. Again there is the danger of focussing too much on the unusual, but there is much to be gleaned about common lives from this type of sources, e.g. by witness reports ("I was doing [perfectly normal thing] when..."), or by trying to find out what was usual by looking at the unusual - when the record states that the suspect did not immediately head to the pub after Mass, then we can reasonably assume that the normal thing was to do just that. Closely connected to this are complaints, e.g. when 18th century priests write disparagingly about young men and women getting it on during pilgrimages.

Another huge thing is archaeology. This isn't just for ancient times, there is also a large amount of archaeology activity focussing on the Early Modern and even beyond. Just last year a fascinating dig came to its conclusion, which tried to find out more about the everyday lives of participants at the "Free Republic of Wendland" protest camp that existed for four weeks during 1980 in northern Germany. Archaeology covers a huge amount of stuff hardly anybody ever wrote about, for instance by focussing on literal garbage: What did people throw away? In what condition was it thrown away? Was it used a lot, or not? What can the materials tell us about the past? And so on. New technologies can also greatly enhance our understanding of the past, like this 2010 paper which shows how we can identify patterns of use in medieval manuscripts by subjecting them to a densitometric scan. We can literally find out what parts of a book were read more frequently, and what parts were only skimmed, how cool is that?

But the main thing is to to use a great variety of sources, and a great number as well. Historians have to compile staggering amounts of sources to get any approximate vision of how common people might have lived their life in the past. By closely looking at this wide variety of sources (diaries, letters, novels, travelogues, complaints, writings and doodles in the margins, official reports, minutes, newspapers, calendars, drawings, leaflets, posters, graffiti and so on...), by contrasting them with each other and finally by always keeping in mind what the context of any particular source was - Who wrote it? When? Where? Why? In what relation was the author to what they describe? etc. - we can try to piece together as much as possible about common everyday lives.

I still got some space left I think, so let me conclude with a practical example. Early Modern Catholics loved pilgrimages: new pilgrimage sites were popping up like mushrooms, old ones were revived, formerly small pilgrimages drastically swell in size. Pilgrimages were so common and so widespread that they were a fixed part of everyday Catholicism for millions of people, and it is quite likely that your average Catholic in, say, 1700 was going on at least one pilgrimage a year, probably more - there were so many after all that it needn't be a large time investment anymore, after all. People could go individually, or they went in groups e.g. in pilgrimages organised by their parish, their confraternity or their guild.

What happened during those pilgrimages? There are a lot of complaints of priests about the unruly conduct of their congregants during those pilgrimages, so from that we can glean that people were probably gossiping a lot. Another important source are the budgets written up for many pilgrimages, which then tell us a great deal - when a lot of money is spent on the church bells being rung in villages the pilgrimage is passing through then it was obviously something that was important to the people, or at least for those deciding what to spend the money on. By looking at the itineraries and comparing them with other sources or archaeological findings we might know more about the roads the pilgrims were travelling on. Extant song books give us clues about what sort of music was performed during those pilgrimages, and maybe there are court records that give us details about the baudy songs that sometimes could be heard in the inn after a long day of walking. You could even go so far and look at the birth records in trying to find out if there is any substance to the occasional accusation of priests that pilgrimages were really the Tinder of their time where young men and women could get to know each other (and sometimes get to know each other *really* well) without parental supervision. If you are really lucky then a Protestant author travelling through the area observes the pilgrimage and leaves some notes on it, even though you have to consider the author's general knowledge of Catholicism and his attitude towards it before taking the observations for granted. There is a wonderful account of an Ottoman traveller going to Vienna in iirc 1662, and he was super proud of his presumed ability to quickly pick up the language, but when you look at his writings it becomes clear that he often drastically misunderstood what was going on. Another example would be the different attitudes of Charles Burney, who recounts visiting Paris during Corpus Christi with sort of a bemused sympathy, whereas only a few years afterwards Friedrich Nicolai from Berlin writes about the Catholic processions of Vienna with open contempt. Yet they are writing about basically the same thing!

It's a lot of work that often enough leaves you empty-handed; sometimes the information is just lost, and you are left with mere speculation. Yet all this work can be extremely fruitful. Just keep in mind that its results are just an approximation, and always will be. The entirety of past experiences is simply lost to us, and there is no way to fully get it back.

I think that your question contains a phrase which very accuratly describes the process employed by historians when they are researching history, namely "piecing together". It's very much like a puzzle with a lot of missing pieces. It's even more difficult than that. You aren't just trying to piece together the pieces you have, you are also trying to fill in the missing pieces based on the ones you do have. So how do historians do that? Well, let's think about how and why we acquire historical knowledge. Anything we know about the past, comes to us through historical sources and historians rely on them when they are trying to piece together a cohesive picture of past events or when trying to coherently support their thesis. Sources come in various forms, but they are essentially anything that contains information about the past. There are oral sources, written sources, archeological sources, artifacts and other objects, etc.

Now ideally, you'd want to combine many different sources. They all have their own strengths and weaknesses. Let's take for example records of toll being levied near the entrances to a big city. These are great sources to accurately estimate the amount of import and export of certain resources to and from that city. That's their strength. However, these will mostly be quantitative sources with very little qualitative information. What that means is that they mostly contain numbers, but they won't provide any context. They weren't created to provide us with context, they were created for practical reasons and to serve a very specific function. Why and how a source came into existence is something we always need to keep in mind and I will certainly come back to that later. So the lack of context within these sources means that you can't really draw any big conclusions. Let's say two cities have a very lively beer trade going which then suddenly stops. These sources can tell us that it did stop, but they won't tell us why. That's why we need to combine them with different, preferably more qualitative sources. Mostly and ideally these will be written sources, something like a chronicle detailing strife between these two cities during the time where the trade between them took a nosedive. It's these types of combinations of sources which allow historians to draw well founded conclusions.

The issue with researching the lives of common people in distant times is that we don't have that many written sources detailing their daily lives. Why is that? Well, we need to ask ourselves who would want to write about the daily lives of the common people and why? You have to remember that this is before history and sociology developped into the academic disciplines we know today. At the same time generally literacy wasn't all that widespread. While the literacy grade really varies in both space and time, it's safe to say that in most regions prior to the eighteenth or even nineteenth century literacy was mostly reserved for the elite and clergy. While we do have some examples of "middle class" individuals being literate and even keeping diaries or owning books related to their craft or profession, they are very rare and therefore also treasured by historians. This is especially true for late medieval and early modern times though, specifically with the advent of book printing simply because it became more affordable to own books and because written sources became easier to create and distribute.

So for written sources with some qualitative content, you'd ideally want diaries written by the common individuals themselves - which again are very rare - or perhaps sources written by members of the elite or clergy who for some reason felt compelled to write about the daily lives of common people. There certainly are various examples of the latter, ranging from treatises originating from budding sociological interests to short snippets written out of frustration with the common people. The problem with this is that this is obviously written from an outside perspective and it's very difficult to tell what's accurate and what's heavily tainted by biases. That's a question historians always have to ask ourselves when analyzing sources. They have to ask themselves who wrote something and why they wrote it. The best way to provide context to the writings of a single individual and to accurately gauge their biases or truthfullness, is by comparing them to other relevant sources. This isn't all too easy to do when there aren't a lot of sources to compare them with, which is sadly a reality when it comes to the history of the daily lives of common people. So we are often left guessing about the factuality of many of these sources.

That's why it's so difficult to research the daily lives of common people. Now on to the good news. There are a lot of creative historians. We are used to solving incomplete puzzles with limited information. This isn't an exception. Like I already mentioned, historians look to combine various sources to paint a more accurate picture because each type of source has its own strengths and weaknesses. Historians who are studying the lives of common people have to get extra creative. They will use sources ranging from paintings, artifacts, poems, folklore, inscriptions, almenacs to garbage pits and epitaths. The Roman epitaphs are a great example of this. They are very human and relatable sources of information and not exclusively reserved for the elite. All these bits and pieces from very varied sources are what allows us to attempt to form a rough depiction of the every day lives of common people.

Still, despite all of our best efforts, there are plenty of gaps in our knowledge about common people throughout history and we are often left guessing. We also often get it wrong. Let me give you an example, for the longest time one of the most prevalent theories within family history of Western Europea was that parents weren't all that emotionally attached to their young children because of how common infant mortality was. This was reaffirmed by a few sources written from the perspective of educated individuals who were puzzled by how common people would just go on with their lives when faced with the death of a child. While there were theories objecting to this because we've found children buried with a toy, some decorum or with touching epitaphs, there were certainly arguments to be made for both. That all changed when we uncovered a few diaries written by lower to middle class tradesmen who supposedly became literate to read books on their trade. These diaries clearly detail their great internal turmoil when faced with the imminent death of their child, often expressing their love for their children and pleading to God to save them. Really quite touching to read. While these are obviously very individual experiences, they did put into question the first theory I mentioned and forced historians to either abandon that theory or at the very least nuance it.

This is why diaries can be such powerful sources when it comes to studying the daily lives of common people. They aren't usually written for an audience which makes it fair to say that they are often more plain and honest, eventhough they are obviously still subject to the potential delusions of their creator. They are also specifically written to detail the daily life of an individual. This combination makes them so unique and powerful tools to historians. So if you want to know more about the daily lives of common people in the past, pray that we find more diaries written by common people ;)

/u/sowser has written about 'History at the Margins' for a Monday Methods thread.

Another Monday Methods post titled 'Can the Subaltern Speak?' was hosted by /u/Commustar

Commustar also hosted a thread about 'Looking at history from the bottom up'