First of all, ensure that you are playing on a high-definition display (720p or higher).
Once Player 1 is in-game, you can join them at any time! Here are the steps to play split-screen multiplayer in Terraria PS3:
As Player 1, start a game as you normally would.
When you spawn into your world, turn on the second controller and press Start.
Select the player account that Player 2 would like to use. If you don't have one, create one first. It doesn't have to be a PSN account! It can't be Player 1's account, though. It has to be a different one.
Select an existing character or create a new one, and you'll join Player 1's game!
That's all you need to do! This will work for up to four (4) players total.