Say sorry.
If you've made a mistake, if you're at fault, admit it. Don't let pride hinder you.

Realize that just because someone is with you, doesn't mean everyone else is suddenly unattractive to them.
It's okay to be attracted to someone. To think someone looks good. That doesn't mean that person is going to necessarily act on those feelings.

Don't cheat.
Just don't. If you'd rather be with someone else, just break up already. It's not fair to lead someone on like that. And you'll most likely be caught anyway.

Have fun together.
Enjoy time with each other. Go out to fun places. Do things you'll both enjoy.

Compromise, Communication
If there's a problem, come up with a solution together. Hear each other out, and try not to assume so much. Think before you speak.