I’m not a fan of problem solving, but if anybody thinks they might be interested in this area of chess, I came across a couple of interesting introductory resources.
Chessmaniac offers a free 101 page pdf book, Chess Problems Made Easy, that deals with two and three movers that takes you from the beginning. Chapter One starts you off with technical terms and then expands on them from there.
You might also want to check out Peter’s Problem World at Chessville. The column is by Peter Wong of Sydney, Australia, a FIDE Master of Chess Composition.
And if you are really into chess problems, the 68-page pdf Handbook of Chess Composition is available HERE.
Chessproblems is a chess problem and puzzle site that allows you to interactively solve and explore all varieties of problems through an interactive applet. Any user can contribute new chess problems through an interactive editing system. You can also select the level of difficulty ranging from ‘Novice’ to ‘Fiendish.’ To unlock the full benefits of the site, free registration is required. When logged in, problem attempts get remembered, so when you view a problem you can see how many times you've tried it before, and how many of those attempts were successful. This information also lets you search for problems that you've not tried yet, or not solved. A forum also exists for general discussion of the site.