Normally, you will get this message if you try to play a used game:
"You cannot earn trophies in this application. Only the first player to use an application can earn trophies. To earn trophies, you must link the Sony Entertainment Network account of the first player to use this application with the PS Vita system."But don't worry, there is a workaround. It is a basic process, but involves deleting previous data off of a Vita memory card.
A website called Pocket-Gamer has a tutorial set up. Click here to see the process.