Pretty simple process really. For removal of trim rings I usually start at the 12:00 position and gently pry at the outer edges, say 2:00, 4:00, 6:00, etc. After a few times prying the trim ring is generally easily removed by hand the rest of the way. Install is similar but I start at the valve stem hole and work the trim ring around until it is all seated with the exception of one area that needs to be seated. That section I give a sharp rap with the rubber mallet head and normally that's all it takes. I then go around the trim ring with a few sharp raps to fully "seat" the trim ring to prevent it from coming loose during travels.
For dog dish/poverty caps and rally caps, pretty much the same removal technique by gently prying again at the 12:00, 2:00,, 4:00 and so on positions. Usually it comes off in my hands by the time I get to 4:00 or 6:00 o'clock. The rubber mallet head aids as a fulcrum and pad to add force to the pry action and also prevents marring the wheel. When installing I mount the cap to the wheel nubs as best as possible until only one nub has not engaged. That is the area I give a sharp rap to with the rubber mallet head. Usually seats well each time.
A bit of practice and it will become second nature to you for removal and installation. Give it a shot and it will work well for you. Great tool to use on caps and rings.
