I purchased GTA V from the PlayStation Store and downloaded it to my PS3. I recently got another PS3. Can I put GTA V on it without having to pay for it again, and if so how do I do it?
Simply sign into your PSN account on your new PS3 and go to the store - from here you'll be able to download the game again.
You'll want to set one of your PS3's as your primary console - this means you'll be able to play your PSN brought games even when the console is offline, however the other console won't be able to (when offline).
If this console is a replacement, then simply set the new console as the primary, otherwise concider which is more likely to be offline and set that as your primary system.