How do I play split-screen multiplayer in Terraria PS3?

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: 

1. As Player 1, start a game as you normally would.
2. When you spawn into your world, turn on the second controller and press Start. 
3. 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.
4. 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 in total.