It depends what contest you're doing(eg. cool, beauty, tough). But I'll try to cover stuff.
Use poffins to increases the pokemon coolness or beauty or whatever to help with the points.
For dancing, you just have to be good at it so practice until you get it. Here's a tip to screw the AIs up:
Try to overlap your steps with each other by jamming the buttons. If one of the dance steps are halfway on top of the other, you can be sure that all of the back dancers CAN and WILL miss their entire step. However, you must be extremely good at the contests to get a GOOD or EXCELLENT while doing this.
For the moves part, here's a strategy:
1ST MOVE: Points of next appeal doubles.
2ND MOVE: Points +2 if first to appeal
Idea behind this:
1. "Points of next appeal doubles" moves give you no points that round, except for impression at the end of the round. Since the lowest performing contestant goes first next turn, and you're VERY likely to go first, this will be a good shot, and will get back the points you should've gotten last turn.
2a. Using any of the "Points +2 if first to appeal" moves gets you four points in this way, and gives you four more points afterwards. This is more effective than the "high score for a low voltage" technique, because it will always get you eight appeal on the second and fourth turn. So it's pretty good, right?
"Charge," then "first" strategy.
1ST ACT: 0
2ND ACT: 8
3RD ACT: 0
4RD ACT: 8
Go first next round, then first hit strategy.
1ST ACT: 2
2ND ACT: 4
3RD ACT: 2
4TH ACT: 4
Yeah, this is long=P
Credit to Serebii for some of this info