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 positively assert that "there is no god", although many atheists believe this as well. People who do believe that there is no god are sometimes called "strong atheists", in contrast to those who merely lack a belief in god, who are sometimes called "weak atheists" or "agnostic atheists" (see 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.