This is a short list of some things all performing groups should strive to do when sharing the stage with another band. When my band opened for a larger group a few months ago, we didn't realize the other group didn't have the same on-stage manners we did. Here are some tips I came up with in the aftermath of our gig.
1. Introduce yourselves prior to the show if you don't already know each other. Chat it up - get to know one another. The business of music is much like any other business - relationships matter.
2. Stick around for the other group's set. I really mean this. For starters, if you're in a small venue, it helps to fill the place up. Secondly, it's just plain rude to leave, and thirdly, you avoid embarrassing yourself by showing up only for your set and then not being able to comment about the other band during your set (if they happen to play before you). If they're playing after you, it's also prudent to stick around and listen. They will notice, the audience will notice, and the venue staff will notice. And heck, they might be really good, too. Finally, you may learn something about them, which could save you some embarrassment due to ignorance down the line
3. This is really an add-on to the last point. If you have friends coming to see you, encourage them to stick around for the other groups too. They'll hear some great music and playing for a bigger audience is considerably more satisfying than just playing for the venue staff and the sound guy.
4. Make sure you're actually performance ready. By that I mean well rehearsed. I was originally really excited to hear the band we opened for. Unfortunately, they were poorly rehearsed, out of tune and in general not very good. It may have been the one time I was glad we were the opener, because I'm not sure I could have opened my set by saying "Wow, I really enjoyed that last group!"
5. Finally, acknowledge the other group. ESPECIALLY if they have opened for you. They are a huge asset to you, either way. Other performers bring other audience members who may just like your music too, which means your fan base just got that much bigger.