Be honest, helpful, and kind. We all want to succeed, but we do this to enjoy making things for people to enjoy. If we just wanted to make money, we'd ditch all this and go into banking.
In order for everyone to take a turn, you will need to spend more time playtesting other designers' games than playtesting your own. But you should be able to get at least one solid playtest of your own prototype each day. If that doesn't seem like it's happening, ask a staffer for help.
If you see a designer looking for testers, join their session before pulling out your own prototype. After that session is done, you'll have a group ready for another playtest, and that's a great time to propose yours.
You don't need to play a full session of a game to playtest it. If you've played for an hour, it's okay to say "I think I'm ready to give you my feedback."
After the designer has introduced their prototype, if you are not comfortable participating in the playtest, let the designer know your concerns. It may not help them much to get feedback from someone who's outside their target audience. But your divergent perspective may provide useful insight. It's good if you can come to an agreement, but you always have the right to step away.
Don't give feedback until the game starts. Ask for clarification if necessary, but actually try the game out before offering suggestions. If you can't let the thought go, write it down and come back to it later.
Be open with your feedback. You may be a game's first playtester outside the designer's friends and family. More perspective from helpful people who are more objective is what they need to make a game that other people will enjoy too.
Give your feedback once and be done. Don't get upset if the designer doesn't seem immediately inclined to act on your ideas. Games are complex systems, and you may not understand all the ramifications of your suggestions. Or the designer may have a particular vision that is critical to their interest in the design. Either way, don't repeat yourself: let the next person speak, or the next playtest begin.
If a playtester tells you they see a problem, they're probably right. But it's up to you to decide if the problem is serious enough to justify what it will cost to fix. And it's up to you to decide how to fix it: You don't have to follow every suggestion, but you should understand the reasoning behind it.