I am not a moral realist, thus I imagine my behaviour wouldn't change all that much.
My motivation to act one way or the other in any situation is based on a few things: my sense of rightness or wrongness, though other factors may override them (thirst, hunger, lust, etc), not on whether or not the act is "truly" right - I'm not sure what that would mean. I am skeptical of rightness being a property of certain acts in the world; I have not seen convincing evidence of their existence.
I nonetheless have this sense of right and wrong that I think about often, and revise according to other things I value (logical consistency being the most significant one, I think).