Bicycle repair is not rocket science but it does take some know-how and tools to do the job right. Even if you only intend to do minor repair and maintenance you may, first of all, want to consider getting a good repair stand and for sure you will need some basic bicycle tools, cleaner, and a good lubricant.
A large portion of bicycle maintenance is simply in keeping it clean. Remember, dirt and grit are abrasive and will cause excessive wear on moving parts. This is especially true of the chain, deraileur, and brake linkage. Bicycle cleaning sounds like a no-brainer but there are some very important things to keep in mind. Check out tips on bicycle cleaning.
Also, it is very important that you keep the moving parts lubricated. This is especially true of the chain and deraileur. But, do not over-lubricate as this will actually attract dirt.
I have found one of the best, all-purpose, lubricants is Tri-flow that you can usually find in any bicycle shop. It has teflon particles in it and the lubricating and penetrating qualities are amazing. For best results make sure to shake the can as directed.
It is also important to check the brake pads often and make sure there is no grit embedded in them. If so, you can usually scrape them lightly with medium sandpaper to remove it. Make sure to clean the wheel rims with a solvent. Then re-align the brake pads.
The realignment takes practice but, with patience, the average person can do it. Both brake pads should touch the rim at the same time, and be flat with the rim, when the brake lever is at about 1/4 to 1/3 way through it's full range of motion.
You may also want to consider a 12 volt air compressor I keep mine in the trunk of my car so it is always handy.
As a rule, I only do simple repairs and maintenance but, like a lot of us, I do like to tinker and sometimes I need advice from a professional. The subject or bike repair is far too extensive for this site so I will leave it for the experts.
There are some tools that I recommend that you carry on your bike for for minor repairs away from home base. Check out the Bicycle tool kit