An atheist is a person who does not believe in any gods. Atheism is the corresponding philosophical position.
Notice that the definition given above does not require an atheist to claim god's nonexistence.
Types of 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.
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).
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, but 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.