How do you determin if you're interacting with a legitimate project?

I have a question for everyone here. Say you hear about some popular project and you want to go and see what all the fuss is about. You visit the web site and your wallet pops up a window, telling you the the site you just visited wants to connect to your wallet.

My question to you is: how do you know that is a legitimate project and not some scam? What information do you go and look for, before deciding that interacting with the project is safe?