An atheist is a person who does not believe in any gods. Atheism is the corresponding philosophical position. This commonly used definition does not assume any positive claim of the nonexistence of a god.
Types of atheism
Main article Strong atheism
A "strong" atheist is one who positively asserts that "there is no god". Strong atheism is the form of atheism that most theists reference in debates, since most don't know the distinction between strong and weak atheism, however strong atheists are rarer than most people think.
As a general concept, god is very vague, with specific incarnations being very well defined. Well defined gods are easy to disbelieve, it's the claim that god as a concept is false that separates strong atheists from most weak atheists.
For the above reason, strong atheism is sometimes criticized for "requiring faith." But this is not necessarily true. One could argue that it depends on how you define god. If by god you mean an infinite being, then you have certain logical contradictions. The omnipotence paradox for example. If you mean a finite being, the strong atheist may deny its status as a god, as it could be surpassed, and may only be very advanced extraterrestrial life.
Main article Weak atheism
A "weak" atheist is one who doesn't claim that there is no god, but instead simply lacks belief in a god. This form of atheism is the most common, and is sometimes called "agnostic atheism" (see our discussion of atheist vs. agnostic). Every newborn baby is (unknowingly) a weak atheist, and remains so until the concept of god is introduced to them.
Weak atheists often argue that theirs is the only rational position, as both theism and strong atheism make positive claims.
Apart from not believing in any gods, there is no official atheist doctrine. There is no atheist pope, no atheist church, and no atheist rules to live by. This does not mean that atheists do not also follow societal and legal rules, or that they are not necessarily religious (as atheism is a component of some religions). It does mean that there is nothing specific about atheism that tells you how you should live. However, there are comprehensive philosophical positions that include atheism as a part of the overall philosophy, secular humanism being the most well-known example.
Not everyone (not even all atheists) agree with the definitions above. For instance, the authors of Evil Bible seem to define atheism as denial of the existence of any gods, or the (positive) belief that there are no gods. Richard Dawkins, author of the God Delusion, does reserve the terms theism, agnosticism and atheism on a Spectrum of Theistic Probability from 1 (I know that a God does exist) to 7 (I know that a God does not exist). In other words, that "atheist", for Dawkins, is synonymous with "strong atheist", as above.