How does one who does not believe in God define what is good?
The witty answer would be: "the same way as anybody else."
But that doesn't really get across what you want to hear.
"Goodness" isn't random, but it IS inter-subjective insofar as a community can define totally random, ethically neutral acts as either good or immoral.
In general, though, people have a pretty solid grasp on what is good in broader categories. We derive that ability from countless ancestors who cooperated with each other as a social species.
Long before we acquired the ability to understand symbols, our distant relations were already reacting positively to pro-social behaviour. You can observe it in other, decidedly less intelligent species.
It's the random stuff cultures and religions have been conflating with morality that generates problems.
Is a woman leaving home without covering her hair immoral?
What about her breasts? Must they be covered at all times in public?
What about male breasts? Or breast feeding?
Since people identify so strongly with cultural/religious norms, they really feel that the random stuff is just as much of a violation as, say, taking what isn't yours or hurting somebody against their will.