Have you already tried entering one and had it work out, or are you still hesitant to give it a shot?
Here's the thing: the system is pretty straightforward, but the bot does a lot of work behind the scenes. When you see the giveaway message, the bot is already waiting for people to react with that specific emoji. Each reaction gets logged in a database, and the bot knows exactly who reacted, when they reacted, and on which server. Then, when the time runs out, the bot generates a random number and picks a winner from everyone who participated. Some more sophisticated bots have extra requirements, like needing a certain role on the server or having been in the community for a minimum amount of time for your entry to be valid.
What's worth knowing is that each reaction counts as one entry, but normally you can only react once per giveaway (though it depends on how each server sets it up). I've seen giveaways where you get to react again if you meet something specific, like leveling up on the server or being a premium member, but that's just how the admins decide to run it. The important thing is there are no weird tricks - you just click the emoji, the bot registers you, and when time's up, you find out if you won or not. Some servers send private messages to the winner, others announce it publicly.