The best way to understand this is probably to think about your own ways of doing this. If one reads the Bible one finds rules of the proper ways to run a system of slavery. I assume that you do not actually think that slavery is moral. But clearly that judgment cannot come from accepting the laws in the old testament as allowing one to read right and wrong off of them, because if you did you would have to decide that slavery is acceptable, and that seems unlikely.
So the same kinds of moral reasoning that you use to decide that slavery is wrong despite what the Bible says, atheists use to determine what is right and wrong, without thinking the Bible is the starting point.