Sound like me 7 years ago when I got my first pair. It took me about half an hour each time to put them in during the first few weeks. Eventually you get used to it, and once you get used to it, it's like riding a bicycle: you'll be able to molest your eyes at will with no twitching. I just went back to lenses this past September cause I got so sick of having no peripheral vision, dirty glasses and no choice in sunglasses.
Right now, I use the tip of my right index finger and pry my eyes open with my left hand and 3 fingers (excluding thumb and index) on my right. I don't use a mirror since I've gotten use to where to poke. Having a paper towel is useful too for drying your right finger tip. It's very hard to get it to stick in your eye if there's too much lense solution on your finger tip.
Hope you have fun, cause 3 months in, they are starting to annoy me again; they dry out way too easy. I stopped using them 6 years back cause they were so irritating, they weren't that good at correcting my vision. Planning on going with hard lenses next year after I run out of disposables...