There's so much going on at Disney, that sometimes it's hard to believe that they're not running all of Central Florida. But actually, Disney is not affiliated with Universal Studios or Seaworld (nor are those parks affiliated with each other). So you're going to have to go the websites for those parks to get ticketing information for their attractions.
To buy tickets for the Disney parks, which include the Magic Kingdom, Animal Kingdom, Epcot, Disney's Hollywood Studios, Blizzard Beach, and Typhoon Lagoon, you can either call Disney reservations (407-W-DISNEY) or order tickets online
here. You could also buy tickets at the actual theme park. A one-day Disney base ticket will get you admission to the MK, AK, DHS or Epcot. If you end up wanting to visit more than one of the Disney theme parks, you could purchase a multi-day ticket, which will reduce the per-day cost.
The water parks (Blizzard Beach and Typhoon Lagoon) have a slightly different ticketing structure. You can either buy these tickets individually or buy them as a "water parks and more" add-on to your basic Disney ticket. The first option (separate tickets) will be cheaper if you only have a one-day theme park ticket.
I hope this helps.