Sometimes, for PDGA sanctioned tournaments, online registration is available where you can prepay with a paypal account. Otherwise, find out when registration is, get there early, and you shouldn't have a problem getting in. I doubt there's online registration for the discin for dogs, but you can probably pay Paul or whoever's running that, if you see them beforehand. I wouldn't worry about not getting in an event like that though, just get there early, to ensure yourself a spot and time to warm up.
As far as your division goes, if you've never played a tournament before, I'd recommend playing in the intermediate division at least once, and if you do exceptionally well right off the bat, move on up to the advanced division.