I'd be careful prying the ring down, Karen. Though Mike may be correct, I've never tried to remove them that way. As Jerry said, the outer ring can be pretty tight to the ceiling material, for whatever reason. Some installations have the fixture inset a millimeter too far, so the outer ring is too snug to the ceiling and aggravating to try and twist off and on even with only an eighth of a turn.
You may have to work at it a bit, trying to grip the thin outer edge, or try some tacky material such as anti-slide sheets commonly used in RVs, and get the ring to turn counterclockwise until it disengages and drops down. That said, Mike's idea might work if only to pry an edge slightly down enough to get an adequate edge grip for turning; but that may only serve to make the engagement ears tighter, whereas pressing upward should help disengage them. Each fixture will have its own balance point and proper technique.
As Jim said, install new bulbs without touching them - as with halogen home or automotive lamps, skin oil on the glass will burn in and shorten their lives. In the past, I've just opened the package and grasped the bulb through the package to insert it in the fixture. The two little bulb wires can be a bit hairy sometimes to align correctly and insert, but don't force them. Using LEDs that don't get hot and rarely have to be changed may be an optimal solution, though I've heard some complain they aren't quite as bright.
-Joel