It's a one question quiz, actually:

Do you want to be a furry? Yes or no?

If yes, congrats! You're now a furry.

I'm actually an asexual furry. So no, you don't have to engage in any sex at all. I like the aesthetic and I've met a bunch of my friends through the fandom as a shared point of commonality.

Probably the biggest question you'll get asked as a new furry is "what is your fursona?" If you say you don't have one, everyone will make a pitch to try to sell you on theirs. (psst Maned wolves are cool.)

For a more in depth explanation, take a look at furscience. They're an actual research institution studying the fandom.