I think you mean "laugh about" and "laugh at".
There isn't a strong difference. "Laugh at" suggests ridicule ... "You're laughing at me" would mean, "you're making fun of me."
You can "laugh at" or "laugh about" a funny movie, for example. But if you're laughing at it, you're probably watching it right then, if you're laughing about it, it might be an hour later, with your friends.
The formula for "Laugh at": I see something or hear something + I think it's funny + I laugh
Laugh about: I think about something, remember something, talk about something + I think it's funny + I laugh
"Laugh with" just means you're with someone, and you're both laughing.