Introduction Round
The first round will judge your Pokemon based on the stat matching the Contest you've entered. Using Pokeblocks to boost the particular stat needed for the contest is the best way to ensure that you'll get a good headstart.
Talent Round
Here, your Pokemon needs to use different moves to impress of the judges and the audience. The moves your Pokemon performs will also affect the Excite Meter on the top left corner of the upper screen. The meter is also affected by other contestants. You're given five turns so you need to carefully choose your Pokemon's moves.
Combos
Use moves that match the contest type and perform combos to impress the audience. The example below is using Salamence's Focus Energy + Stone Edge combo.
Cool Moves
You can also moves that can startle other Pokemon, making them lose their appeal or make them nervous that they won't be able to use their moves.
Audience Excitement
All participating Pokemon in the contest can affect the excitement of the audience. While cool moves and combos increase their excitement, using moves that doesn't match the contest type or the Pokemon's stat will have negative effect instead.
Since the other Pokemon contestants can also affect the overall crowd excitement, you need to time your appealing moves so the audience's excitement gauge will be full when your turn comes. This will allow your Pokemon to perform a special move that will give you a bonus.
If your Pokemon can Mega Evolve and the audience's excitement meter is full during its turn, it will Mega Evolve, displaying a very impressive move that will earn you an even greater bonus.