Select the cache, then hit the menu button. Scroll down to "delete" and select. If you're downloading pocket queries onto your gps, be sure to select the "not found" option so that the website doesn't load them back onto the gps. (Marking the caches as "found" won't delete them from the gps.)
You can hide geocaches you've found from the geocache list without deleting also. Go to the list, hit the menu button, select "Sort & Search", select "status", and uncheck "found". Hit the back button to get back to the list, and all the caches you've found will have been hidden.
I prefer to leave the caches I've found around my home area on the gps, because I can use the info to make sure I'm far enough away from existing caches when I hide a new cache. It comes in handy if you want to hide caches.
Good luck!