Atheism
The only belief that is definate among the many many individual types of atheist is the belief that there is no supreme deity or power. There are actually two kinds of atheist: strong atheist and weak atheist. Strong atheists believe that such-and-such god does not exist or that no gods exist. Weak atheists are simply doubting that such-and-such god exists, usually because they have seen no evidence for the existence of any god or becausse they were raised atheist. The difference: "The Christian god doesn't exist," vs. "There isn't any evidence that the Christian God exists."
Agnosticism
Agnostics believe that humanity cannot know whether or not a god exists or that humanity could know but we don't have enough information to decide. Either way, it's kind of an "I don't know and doubt I ever will" stance.
Freethinking
Freethinking is not a belief or lack of belief like atheism, but more like a system of thinking that is commonly grouped with atheism and agnosticism. Freethinkers assess individual situations without making a generalized stance on everything (instead of "I'm an atheist" or "I'm an agnostic") and test everything by the same set of standards, like the scientific method. This is personally preferred by me, but everyone has their own decisions to make.
If there are any questions on any of these, please email me and I will try to put up some more information.