The question that comes in my mind right now is: What would make me or someone believe in something? What triggers a belief? I really am curious.
There are various things you can look at to try to answer this. People that have converted, left or taken up faiths later in life could be interesting, however things there tend to be a bit more anecdotal. If you are going to take the less science based routes then studies of where religions collide are great as the mingling and reworking of things sees all sorts of things shake loose. The spread of various Jesus focused religions in Europe and the various blending, appropriation and in some cases eradications of local beliefs are good stuff to read about, Scandinavia/nordic countries being more recent and well documented but there are other interesting examples like Ireland (the history of rag trees being my favourite) and the classic Saturnalia becoming Christmas and various spring festivals tending to become Easter. The economic systems that allow certain religions to flourish, exist and thrive are also necessary to consider as part of this, previously I mentioned the idea that the fall of polytheism might have been a more economic one, basically the same as why large corporations can take bigger hits that smaller ones. Also beyond that the incorporation thing some have argued might have happened in Christianity both early on (there is some discussion about John the Baptist and Jesus, though I am not inclined to argue that one) and later stuff like the Scandinavia/nordic countries already mentioned. Even more recently some of the things going on in various Asian/oriental countries is enough to raise an eyebrow.
There have however been many studies on various aspects of this, and it plays into a lot of other fields (security being a good one for me).
Anyway in psychology and sociology it is a massively complex problem (how the mind and groups work respectively) that you are ultimately trying to solve so it often makes sense to start at the edge cases and broken things.
For sociology then two good ones are tribal beliefs, even better if they have not had any/much contact with the outside world though those that have suffered missionary* and other groups are still valuable sources of data, and those that suffered in "reeducation" programs like those native Americans and native Australian aboriginals were subject to in comparatively recent times. It makes for some sad reading, however if the aim was to nerf tribes and levels of tribal beliefs then it did well there. The small tribal beliefs stuff, current and historical, gets interesting. It has been observed usually to start as natural forces and then get amalgamated into greater and greater concepts until you wind up with either a pantheon or a singular god, or some kind of death and rebirth metaphor (I will go with a Lion King quote here "When we die, our bodies become the grass, and the antelope eat the grass. And so we are all connected in the great Circle of Life").
Psychology takes different approaches at times (though being a different science that is to be expected), we could talk about those with brain injuries that might gain or lose things which can be interesting but are not that useful for an introductory discussion and developmental psychology has a lot to say about this. The security thing I mentioned earlier has two related things in the lion behind the bush problem and the false pattern recognition problem, something you might be more familiar with if I said Skinner box as that concept crops up in games and the discussion thereof a lot in recent times. The lion behind the bush problem is that humans are superbly well adapted for living on a savannah some 10000 years ago, less good for massive city dwelling setups; the average person can on immediately count things up to three (see also why most writing systems, and certainly the successful ones, have letters/characters/runes/pictograms composed largely of less than three strokes), the concept of 10000 vs 1000000 is means very little to them intuitively, most people do not consider beyond about the horizon as a distance and the awareness shrinks rapidly before you even get to that, most people like themselves a lot, their immediate family and friends a slight bit less (or maybe more at times), their tribe or functional equivalent a great deal and beyond that it is a bit hazy).
*people like to look at the westboro types when they want to consider the nutzoid damaging set, however you really want to be looking at what various anti GMO and anti gay groups are doing in Africa, and they often claim a religious basis for their acts.
http://www.alternet.org/story/15372...he_anti-gay_bills_sweeping_sub-saharan_africa has some more.
Developmental psychology then. Human rights setups will tend to favour those wishing to teach their kids what to believe and with a history like those reeducation things mentioned I can not blame them, though as mentioned I still find a lot of things done under the shield of such things to be horribly distasteful. Again more broken things are good to look at here so look for things where people grew up being taught to be racist, whether intentionally or by osmosis. In these sorts of discussions I prefer the racist thing to cult recruitment practices as I am not inclined to call all religions cults at all, however there are some serious overlaps at times. Or if we want to go to religions then see phrases like "the family that prays together, stays together" (though I might argue it is the opposite way around, mainly as the power of prayer is not something I like and when not careful it also leads to things like pray away the gay).
Religions as social and economic operations.
I already mentioned the Jiyza tax that various Islam practising states levied on those that wanted to keep their religion and how it drove down belief rates there. Most here though are European and thus their baseline to compare things against is Christianity which says not a lot about economics beyond probably best not to be a church money changer and giving to those less fortunate is a good thing. You look at something like Islam and it has a pretty full economic system baked into it, a bit simplistic for my liking and not one I can get behind fully (though I can not expect much as 1500 years ago they did not have the maths and computing power that we have today) but if you have to pick one religion to base you system on then you could do far worse and I am not sure what the better options might be among the popular ones, and necessitates a different approach to things. The caste systems of various more eastern religions are also interesting, even better if you want to contrast it to feudal systems seen in parts of Europe. I say that though but churches invented some pretty good systems of economics ranging from the basic tithe (the accounting/recording of which provides lots of good information to this day) to the first traveller's cheques/quasi bank accounts for pilgrims.
http://thefinanser.co.uk/fsclub/2011/08/we-are-knights-of-the-banking-table.html
Even without that though churches do somewhat well for meeting places and then as now success in work is still a good chunk of who you know and luck/meetings, with what you know often coming a distant third.
In psychology there is a concept called Maslow's hierarchy of needs, you have probably seen it before and you can see it again
https://figures.boundless.com/29841/large/Maslow's_hierarchy_of_needs.png
Like a lot of older psychology its usefulness is debated by some but it is not dismissed by any means and I find it useful here. On the bottom and thus the things that people are supposed to want to sort first of all includes food. Or if you prefer a truly hungry person will do a lot to sort that and if you are wandering around a hot desert like the middle east of the times a lot of religions cropped up then being hungry is a decent possibility, doubly so if you are poor. Being a hot desert and without much to preserve food then pork is a bad plan, however back to the needs pyramid a hungry person will do a lot... appeals to logic that eating suspect pork is not going to work as well as some kind of religious edict, one also enforced by society, that the sky fairy/fairies will not be happy with you eating it. Religion as law enforcement, especially when I do not have helicopters and planes to move my army and messages consist of carrier pigeon and hope or stick a dude on a horse and hope rather than speed of light anywhere in the world is not a bad thing either. Less cynically churches and religious organisations in general (right down to the tribal wiseman type setups) often did do a lot of what is now called public works (building roads, canals, draining marshes, running markets...) and a form of welfare (alms for the poor and all that, or back to Islam then it is baked right into it as a fundamental tenet), as well as the record keeping (records of births, deaths and marriages will tend to be church records of births, deaths and marriages after all). The hot desert no longer being a problem for pork is an interesting one and possibly a nice historical example of a legal concept at work -- law makers have a variety of goals, sometimes it is stemming a short term problem and laws are then enacted, altered and repealed (or not and trouble ensues) as such and other times they are fairly fundamental for the working of society and will be for as long as anybody can consider. While I am at it I do have to say I have to find what could almost be a strawman argument of "if I didn't have religion then I would be a bad dude" to be quite amusing, that or an indicator of some flavour of psycho or socio pathology.
To that end I would probably argue a combination of primitive psychology still being at play, upbringing, societal pressure/desire to join a group, all tempered by economics and a bit more historically then a type of law enforcement. Anyway this looks like it is turning into a wall of text so I will cut it off there.