There are several ways to get tickets:
Play the game
Save your game, quit, and re-launch it. Re-load your save, and viola! More tickets!
They are awarded at a rate of a ticket for every seven minutes, and you can claim up to a maximum of ten at once. This time does not include being in menus, so you can't just idle the game and expect to receive them.
Another way to get tickets is to add friends. As I answered here:
You get seven for originally registering (and having them accept) a new friend. After that, you get an extra ticket for every 40 minutes they play.
This time is combined across your friends; eg. if one plays 15 minutes, and another plays 30, you'll get a ticket, even though neither of them played 40 minutes.
Most trophies award you with a ticket or two when you hit their achievements. Several trophies have their requirements available to be viewed, under Info --> Trophies, so you can see how close you are to getting another one, and its ticket rewards.