I found that all the following step were much easier for me using a heat gun while keeping the pull on the screen with the suction cup. Basically heat up a section, put the suction cup on, keep pulling the screen upwards on that side, while using the heat gun to continuously heat along the side. It came nicely off, one or two inches at a time. Once I had a whole side up, I just put some of the picks in to keep it up and continued along the side, heating, pulling, heating pulling. This obviously only works if the screen is not totally shattered. Mine only had two cracks.
I had a screen on an iPad 4 that was so shattered that I literally had to spend 2.5 hours picking every single piece of glass out with tweezers after pulling the few larger pieces off with tape on them. Sometimes you need a lot of patience to be successful. The final cleaning out of the sticky tape along the sides is also very important once the glass is removed. Or the new screen will stick out an/or not go in neatly.