Knowing how to maintain your bikes and having an idea of when to replace chains, etc will increase your enjoyment of riding (fewer worries about being stranded by a mechanical) and increase the lifespan of the bike. Lennard Zinn's books on bike maintenance are the go-to references. He has a bunch of them out there. They may be available at the library, but may be worth buying used so that they are available when you need them. There are also a lot of online references, but I personally find doing repair work off of the computer challenging relative to a trusty book you can get greasy and have on your workbench.
The most commonly neglected maintenance item that drives up repair costs is the chain. If the chain wears too much and then needs replacement, it may require changing out the rear cassette and chainrings at the same time. Chains stretch over time as the individual links wear and get further apart. The teeth on the gears wear with them changing the effective spacing of the teeth (left long enough, they can look like little shark fins). Put a new chain on that and it no longer meshes with the gears and things go downhill quickly with poor shifting or even the chain being pushed off the gears altogether. Basically, if you've got 1/8th of an inch stretch or more on your chain as measured at the pins over 12 inches of chain, replace it; at 1/16 you should start paying close attention and looking for deals on a new chain (they can be super cheap ones for the most part unless you are riding the tour de france). Depending on your riding conditions, how well it is lubed, and rider power, this happens in about 1500 miles. Changing your chain more frequently will make the whole drivetrain last longer and save you $$.
