There's not really anything you have to do. We like animals and anthros, maybe some other stuff too, but otherwise we're kinda normal. The main thing that dragged me to furry, other than finding that some of the art is awesome, is that I've always been a fan of animals/anthros in books and cartoons. I will guaranteed care more about an animal story than an equivalent human story (even if it's animals that might as well be human). I think the typical start is to create something furry-related (draw, write, fursuit, whatever). Considering I can't draw people and I started out with anthro dragons and birds, I was pretty much destined for furry.
A fursona's fairly common, just something that can represent you for when those situations come up. You don't have to have one (if you prefer just being as yourself, or to be perceived as a person). And there's nothing saying you have to have someone who "is" you or some alternate version of you. It just makes it easier since we're so fast to associate an avatar or prominently-displayed character with someone as if it was them. Could be an existing character you like, could be someone specifically created to represent you and you only. My fursona has changed a few times, first it was a sunner from Riven, then changed to a wolf and fox and rabbit. Wasn't until Oct 2007 (over 6 years since I was known to be a furry) that I decided on my current squirrel fursona of Folgy. Then it took another three years before I was really sure of it.