The limit screws don't move the derailleur unless the derailleur is actually touching the limit screw when adjusting, but that's not a great idea. If the chain is over shifting, turn the correct screw ('H' or 'L') 1/2 turn clockwise ("in"), then try shifting again. If it still overshifts, try another 1/2 turn.
Park Tools has a tutorial on all the components on their website.