I'm in the process of doing it right now myself so I can only tell you a bit about what I know or have read. There are many other more experienced cyclers who can tell you more than I can. Most of my info comes from:
Either way, you'll want to get a water test kit that can test Ph, Ammonia, Nitrites and Nitrates. Its a must to have for cycling (and fish keeping in general). Get a liquid test kit if at all possible as the test strip kits aren't very reliable and thus will potentially miss-inform you of the cycling progress or lack there of.
There are about 5 methods of cycling and I won't mention them all here but the above link has all the info. Cycling your tank is pretty important, especially if you don't want to do a lot of big water changes all the time. There is a "fish-in" method where fish are in the tank while its cycling. This method does have the downside that it can be stressful and even deadly to the fish if your not on top of things at all times! I don't personally think this is a great method.
I'm using the "fishless cycle using shrimp" method. Its pretty easy to do. All you need is a raw shrimp from your supermarket, you put it in the tank (preferably in a mess bag) and wait for it to rot. You keep testing the water until the values are right and the cycle is done.
Note that cycling a tank can take between 4 and 8 weeks so you have to be patient. There are also "bacteria starter" kits which have mixed reviews on this forum. The general feeling is they're aren't overly effective unless the bacteria is still alive, and it isn't. You can get powdered drops and some liquids which claim to help bacteria in your tank which is an important part of cycling your tank.
Good luck. You don't have to be a chemist to do it (I'm certainly not!) but the more you read and the more you test, the better off you'll be. Good luck!