Instructions
Play through the game until you find a save point if necessary (not every game allows you to pause and save at any given time; for example, Japanese role-playing games tend to require save points).
Press "Start" on your controller to pause the game.
Select the option to save. Some games may only allow you to save one file per PSN account while others may let you choose between multiple saves. For example, singular save file games may only have the option to "Save and Quit," but multiple save file games will let you save and then pick a slot on your hard drive.
Press "X" on the slot selection menu to pick your slot.