As a fairly petite, 20 year old virgin, I was really anxious about insertion/removal at first. Once I realized that I couldn't hurt myself with it though, I managed to get past my nerves and learned pretty quickly. I found that the punch-down fold is easiest for my short fingers to keep hold of, and that the band-aid approach (quicker is better!) made for less stressful insertion/removal.
I also solved leakage problems pretty quickly. First, I learned a lot about the shape, etc of my vagina after spending so much time fishing around in there and I used that to my advantage - for example, I insert following my natural angle, which makes for a better seal. Also, I found that it pops better if I push it higher up; presumably I am wider farther up so there is room for the cup to open.
Best of all though, using a cup seems to have cured my mild, chronic yeast infections! Presumably, using tampons or pads for days was too irritating. Tampons were dry and scratchy and pads were too hot and moist. My daily commute by bicycle probably exacerbated it as well. With a cup there's no irritation and I'm dry and clean all day.
I've also found that using a cup has made me more aware of my vagina - what it's doing when it bleeds, how it is a part of my body, my attitude towards a body part that makes me biologically female. Sexually active women probably don't experience this, but for someone like myself with no sexual experiences, using a cup has been thought-provoking.