Usually when we study history, at least in the biggest books and documentaries. Teachers focus on great people, on those who created macro processes.
Although this is cool, I would like to know how to study the history of rites, rituals, everyday objects, clothes, food, the words people used with each other, the songs they sang, the kinship hierarchies, the distributions of power in society...
How do you historians make this type of analysis?
Following the sub rule, trying to make it, as specific as possible, I would like to know, for example, how we know that it was Baghdad in the golden age of Islam. What bibliography could we use to try to build this world in our heads and paint with words?
Well, first of all, I actually happen to know of a PhD thesis you might really enjoy reading. It's called "Social Life Under the Abbasids" by Muhammad Manazir Ahsan. The whole thing is about everyday life in Baghdad during the "Golden Age" of the city in the early medieval period (specifically 786-902 CE). It's a little old (1973), but it's full of such rich details that I relearn so much every time I read it. The chapters are as follows:
The first chapter should help you figure out further reading, while the rest should be full of things to help bring the world of Abbasid Baghdad to life for you. I should stress that there are probably lots of more updated sources out there, but this is a really good one I've found for a general overview of social life and customs.
To answer your question more broadly, historians have to get creative looking at lots of different sources to learn more about everyday life. These include literature, archaeology, wills, economic and trade records, and passing references gathered together from reading many different types of texts. With some periods you get lucky and get a text full of everyday details (albeit usually about the elite, for example The Pillow Book by Sei Shōnagon for court life in Heian Japan). Sometimes literature will include many incidental details about everyday living, whether it's saints' lives hinting at local customs or poetry for kings listing all the foods they ate. Of course, historians using literary texts have to be aware of tropes, exaggerations, and both fantastical and anachronistic elements which might complicate using these sources. That's why other records, like economic and archaeological data, are so important too!