The Film Developing Cookbook and The Darkroom Cookbook are probably the more complete and easily obtainable overviews of the basic concepts of B&W chemistery. They function very well like a roadmap: such product does this, such product is meant for that. They also deal with issues of methodology: how long to wash, when is fixer exhausted, etc.
Here's my 2-minute summary for negative/positive silver gelatin processes (excluding lith printing which I am not knowledgeable with).
The keyword for everything is SLIGHTLY. You can have extreme effects with B&W chemistery, but most qualitative aspects of B&W processing are subtle. The second keyword is TRADEOFF, for instance you can have finest grain or the fastest film. But you won't get both aspects at the same time. The last keyword is CONTROL. Use the scientific method and try to observe one parameter at a time; be consistent in your processing; know what you are doing.
The mother of all decisions is the film/developer combo. It is rather important in a negative/positive process because screwing up here impacts the rest of the toolchain. I won't repeat the exposure/development principles here, but you can find everything about it by reading books about either the Zone System or the Beyond The Zone System (which are more or less the same thing).
To make a brief summary: with film development, you are mostly doing a tradeoff between fine grain and sharpness of contours. If you have more of one, you have less of the other. Corollary to this fact, is that some developers will increase the sensibility of the film, and others will reduce it.
In terms of image structure, you thus have three broad categories of film developers:
1) fine grain, lower sharpness (Perceptol, Microdol-X)
2) medium grain, medium sharpness (XTOL, D-76)
3) bigger grain, better sharpness (Rodinal, HC-110)
Within each of these categories, you will find some developers that increase (Acufine) or decrease film speed (Pyro). So that gives you 3x2=6 basic types of film developer.
With respect to methodology, most film development procedures are meant to give you a film speed that's close enough to the ISO one advertised on the box, and which will give you a contrast suitable for printing your negative on paper.
Paper developers: paper developers is a less hotly debated issue, and is something that you may or may not want to care about now. Start with something, anything, and think about trying something else later if you want. Paper developers have some impact on the tone of the final image, the maximum black you can extract out of a paper, and its contrast as well.
Other chemicals: each film or paper developing sequence requires at least stop bath and fixer. For some reason, stop baths have recently been a hot topic. And by hot, I mean epic arguments on internet forums. Anyway, the whole point is that you want a reliable method of stopping the process of development. A weak acidic solution is the lambda method; some people prefer doing a couple of water rinse. Whatever you choose, please don't start arguing about it online, you will just suffer for nothing.
Fixers: there are two main types of fixers nowadays. The traditional ones are based on sodium thiosulfate, work more slowly, but are sometimes necessary for certain toolchains. Most people stick to a fixer based on ammonium thiosulfate, which works faster. Finally, although these two previous types of fixers are in an acidic solution, alkaline fixers exist as well and are favoured by many. Needless to say, these people do not use an acidic stop bath. You might find some bickering about whether acidic or alkaline is preferable.
Toning: toning is a procedure whereby a solution alters the color of the silver image, not the paper base. Certain toners like polysulfide toning (brown toner) increase archival stability, but people bicker sometimes about whether selenium really helps or not. Toning is a complex issue, and Tim Rudman wrote the book about it, called The Photographer's Toning Book.
Washing: another topic that pushes hot buttons in that it matters for archiving photographs. The basic line is that too much thiosulfates in your photographic material will deteriorate it. That's why you need to wash films and papers after processing. Solutions like hypo-clearing agents will speed up this washing. Again, not something you want to get too hung up about in an online forum. But you can figure it out for yourself by using test solutions for residual thiosulfates.
If you want to have an amazing, complete reference on the chemistery of silver gelatin processes, down to the level of ionic reactions, molecules, and so on, read Grant Haist's "Modern Photographic Processing." It is a comprehensive survey of the scientific literature of photographic science written by one of the foremost expert in a rigourous, yet accessible voice.
