Rock climbing
Hang from a pullup bar (wrap a towel around it if you want to make a wider grip)
Pullups/towel pullups
Finger tip pushups
Fist pushups
Wrist curls
Deadlifts
Farmer's walks
Grip devices are sold at most stores like sportschek or you can order them online. I think the actual ones the PSP staff use must be ordered online.
If you own some weights try adding a couple layers of tape around the handles after every workout.
Just some stuff that worked for me. Make sure when you do the test you get the PSP staff to help you set it, and wipe off the sweat both on your hands and on the dynamometer. I failed thanks to an incorrectly set one. Most people, however, will have no problem passing it, so don't sweat it too much. Only two people in my platoon failed: me (previously had tendonitis) and another guy (previously had a major operation on his forearm).