J.T.
Hello!
You need to get some dead leaves in there and/or cut grass. The acidity from the leaves/grass will help speed up the composting of the food items and help relieve you of the gnats. Try leaving the compost uncovered for a few days as the natural sunlight will help heat up the compost which will also deter the gnats somewhat. You shouldn't need to turn the compost but once a day.
Another good thing to start is worm compost bins. Get tons of newspaper, shred it up, and place within any large container. Get several worms (one friend started out with a dozen) and place them in the container. Within six months, you should have lots of worms and those are wonderful to put into your garden along with the compost.
Best of luck in your gardening endeavors. If you'd like to come to an upcoming plant swap next month, let me know and I'll send you an invitation.
-Jen