So there's a karaoke party tomorrow night and my ex (who cheated on me) is probably gonna show up with the other guy. (We've been broken up for about a week) The reason for the party is to celebrate our dance group's recent performance. I have been dating and gaming other girls and I'm almost over my ex.

Yes I do need to go to this party... it's in honor of me because I'm leaving their dance group (I can't stand seeing that other guy and a majority of the dance group isn't fond of him either.)

So what should I do when I see them there?

Depends on what your objective is.

Do you want to make your ex jealous? That could be an objective of yours since, although you claim to be "almost over her", you probably aren't since you're taking the time to ask us. If it is, just make sure you're seen having fun with other girls. Not necessarily make out. Something like being seen giving a girl a piggy back ride, and laughing with her would be efficient (without making it obvious you're doing it to rub it in her face).

Or do you want to just be friends and convey you don't care she's dating another guy? In that case, you can go talk to them and be a gentleman about things.

Or if you're a little twisted, you can do the above. Then in the middle of the friendly conversation say something like "Oh hey you know what I learned from my psychology class? That past behaviour is the best predictor of future behaviour. And by the way, she cheated on me." Then you quietly walk away.

_________________
Before she can respect you, you need to respect yourself.

Love that ^^^^^

To be honest not going is just going to show you're avoiding her, thus letting her know you're not over her yet.
So go, but keep your cool.
Make sure you're polite if she talks to you, but don't try to start a conversation with her. Amog her current boyfriend if given the opportunity, but don't try too hard.
flirt with other girls and run your game as much as possible, make this your bachelor party in your head.but make sure you don't look over your shoulder to see if she is watching, she will notice and it will devalue yourself. Keep in mind that doing that will trigger jealousy, and she might try to get your attention by doing something with her new boyfriend. Ignore it, play it cool, or ull fall into her trap.
Look good, smell good, smile, be interesting, be unpredictable.
this is important. Refrain from alcohol. Alcohol will numb the pain of seeing her with someone else but it will lower your inhibitions, the last thing you need is to knock the guy out or make a scene (even though it probably sounds very appealing right now).
And ultimately, if you have a very good looking friend, or even a love interest, bring her as your date, if its just a friend bring her as your pivot, the goal is to make her notice you're happy and you don't need her, no matter if your goal is getting over her or getting her back, but she cheated, remember that is not the PUA's fault, it's a flaw in the womans character.

Credentials: ex broke off with me a week ago after two years of dating, is already sleeping with another dude, her boss.

Also after you get home from the party, watch the movie forgetting sarah marshall, it's the ultima breakup movie for a PUA