Hey /r/askhistorian,
The 19th century has become my favorite century, mainly because I've been reading fiction mostly from that time period, set in Europe. And I guess reading books set in the 19th century, and written by 19th century authors, is one good way to get an insight into every day life back then.
But what other ways do you recommend? I've been thinking about letters as well, but how do you get a hold of them? Are there books by historians that quotes letters?
You need to first recognize that there are many different types of lives going on here. The life of a peasant in Poland will differ mightily from a noble in France whose life will be very different than a factory worker in England. Part of the challenge is also the difficulty in finding primary sources from certain segments of these societies. Not many sheppards in Scotland are going to be writing memoirs after all. In this case, things like letters tend to leave out a great deal of the population.
Finding old letters and newspapers is a great place to start though. Lots of these resources are available in collected form online, and many good histories include excerpts as well. I'd recommend books focused on individual countries or regions for the type of detail you should want though. Broad stroke histories tend to forget the smaller people. Luckily, the 19th century is a period where the common man began to flourish and exert their political will, which means there's lots of good histories out there that cover the marginalized portions of societies.