The joy of non-linear editing is you can get shots anywhere and "splice" them together later on, so you can mix footage of a great gig in with staged shots etc. Obviously, when you're making a music video, it helps to have the various changes on beats, and preferably in a sensible bar progression.
What you can do is limited mainly by your imagination and time, but obviously, what software you have access to plays a role too.
If you want to specifically go out and get shots, then it'll probably help to sketch out a storyboard.
Get a tripod. There is a place and a time for shaky video, but it needs to be intentional and there for a reason.
You can make a "ghetto" dolly out of little more than an office chair and a friend to pull/push it; this is handy for those shots where you zoom the camera and move the camera at the same time, giving that effect where the background zooms away or zooms in, depending which way you go.
Don't forget to think of different angles, and as with stills photography, light is very important.
On-camera sound is usually pretty bad; you either need remote mics or studio-recorded tracks, which you then sync with the video (well,
vice versa really).
Much like with stills photography, it's usually better to fill the frame with your subject; you're going to get much better video from the front or even on stage than from behind a crowd of heads.
Good luck!