Turn the question, how does christians know whats right since the book tell them to do so much evil, kill non-believers, kill gays, beat bad children and so on. I've yet to meat anyone living after biblical morality.
Well it's simple, like the theists, atheists have their own subjective version of morality.
Two atheist may have two different opinions about morality, but the same can be said about those who believe in God, just look at the hundreds of different interpretation of God's words, let's take killing for example, some may argue that it's forbidden and wouldn't kill even to protect themselves of their family, other would gladly kill for their faith and other would only kill for self-defense. Morality will vary from one individual to another, religion is not a concrete path but more of a general direction in my opinion.
On a personal note, I believe that we human are unable to comprehend God, so I prefer to keep a critical view on what's considered as "canon" in the book...
I can not speak for others but I have a somewhat unusual take on morallity. I have Asperger's Sydrome(a form of high functioning autism) so I experienced delayed social development and empathy. Because of this I've had to structure my morallity on something other than empathy. For me the results are as follows:
1.Life is of the highest value, without it there is no meaning, value or really anything 2.My life is shared with others i.e. no man is an island unto himself (this is one of the reasons people feel sad when someone close dies, they have, in essence, lost a piece of their self) 3.Degrees of connectivity are important but ultimately all are connected
On this rational basis I have built many other principals but those are more subjective and experience based, these three concepts are what I feel to be a universal basis for morallity. Some use the concept of an afterlife to justify actions that would otherwise violate morallity, this is a very dangerous line of thought as it can be highly destructive. I do not intend to disparage religion, simply those that use it as an excuse. I wash my hands of no action, I learn from the past and move on. No regrets, no justifications, just life and growth.
There's a reason that the Golden Rule (treat others as you'd want to be treated) crops up in so many religions... because it's common sense and empathy that are really at the heart of morality, not checking in a rule book.
Remember the British were all crazy about the way Zulu warriors would cut open fallen Britt's stomachs. The Zulu did it to free the spirit trapped in the body, the British called it multilation of a corpse.