how to fix gear ring that over-jumps
Your issue sounds like a worn chain/cassette.  Take the bike to your LBS (Local Bike Shop) and have them look at it. You can also check yourself to see if the rear cassette teeth look like sharks teeth, that's generally a good indicator of wear.  Here is another post that may help you.  

Generally skipping teeth is a sign of a worn cassette/chain, but it could also be adjustment issues from the derailleurs.