Hello,
The first is...What do Athiest believe?
An atheist has no beliefs (at least pertaining to atheism) but rather an atheist has just one disbelief. The disbelief in God or gods. Atheism is different from other philosophical positions in that it is the only one that comes to mind which is not an affirmative position. Atheism says nothing about how the world is, but merely how it isn't.
The second question is why do Athiest believe the way that they do?
Well I suppose that depends on the individual, and can vary widely especially since there is no "atheist doctrine" to give us those kind of answers, however common arguments for atheism include:
The Problem of Evil is perhaps the oldest argument for Atheism.
http://en.wikipedia.org/wiki/Problem_of_evil
Other common arguments are:
-Argument from burden of proof. That because atheism is not an affirmative position, that the burden of proof rests upon Theists. Burden of proof which according to atheists has not been satisfied.
-Historical arguments that claim that because most religions throughout history have eventually become obsolete, that eventually most contemporary religions will as well.
-Naturalistic arguments, argue that because most things can be explained with natural scientific explanations, that God is logically unnecessary.
lastly How does the Athiest belief affect their lives and influence the lives of those outside of their communities? Thanks
There are many political organizations composed primarily of atheists. The goals of these groups differ but typically they leverage political pressure to support a more secular, or pluralistic direction in their respective communities. There also exist atheist charities, which donate to various causes.
Examples can be found here: http://www.squidoo.com/Atheist-Charities
Outside of these examples, atheism generally does not affect the lives of atheists that much. Aside from a vocal minority most atheists are often indistinguishable from other citizens, and many atheists will relegate their atheism to casual conversations or debates.