It really isn't that difficult as long as you have basic mechanical aptitude, e.g. you can turn a screw without stripping the threads, and you know that you can't over-torque smaller fasteners or they will break.
Edmunds has books for just about any make of car that will give detailed instructions about how to replace just about any component. Many car vendors now even have free factory repair manuals online.
Of course, you have to be able to diagnose what has failed in the first place. That does take a certain amount of experience and the ability to think analytically unless it is obvious.
At a minimum, you need a set of open/closed end wrenches and a set of 3/8ths inch sockets along with a socket wrench and extenders, a set of 1/4" nut drivers, as well as regular and Phillips screwdrivers. If you are going to work on modern cars, you will also need a set of torx screwdrivers or torx extensions for your nut driver.
All of these can be purchased at Sears at nominal cost. I would recommend getting the Craftsman tools because they are high quality and have a lifetime replacement guarantee. You can buy similar tools elsewhere, but you have to be careful to only get high-quality ones. Bad tools will result in stripped fasteners and lots of hassles that will quickly cost far more than the cost of decent tools. You should be able to pick up the basic stuff for less than $100.
Here's a starter set for $50:
http://www.sears.com/shc/s/p_10153_...4&i_cntr=1331510589580&sid=IDx20070921x00003a
And here's an even better set for $120:
http://www.sears.com/shc/s/p_10153_...921x00003a&ci_src=14110944&ci_sku=00927006000
The best thing to do is to start out with basic maintenance chores, like changing the oil, changing the air filter, replacing brake pads, and the like. As you gain more familiarity, you will soon be able to tackle more difficult tasks.
Much of what you need to do will be underneath the car, so you will also need a decent jack and a set of jack stands before too long.
You probably know one or two people who work on their own cars. They can be a great help to get started. And they can help out when you inevitably get stuck. Most of the time it just takes a bit more "persuasion" than you think is necessary. A jar of hand cleaner like Go-Jo and a pair of mechanics gloves also come in handy.