I use the BRS thick gel glue. As some others have said, drying the bottom of the plug/whatever you are putting glue on will help. Once submerged, the glue should form a bubble with a very very thin solid membrane - it should be almost malleable to your touch, but too much pressure will "burst" the bubble and ooze out glue.
When you make contact with the rock/surface you want to glue it with, push down and TWIST - the twisting motion will "break" the thin solid layer of glue and cause the liquid to ooze/spin out in between the frag plug in the rock. Hold in place for 10-30 seconds, slowly try to let go and see if it is sticking. May take a few tries but you'll get the hang of it.
Yes, you'll most likely get glue all over your hands/fingers the first few times. I use nitrile gloves now.
Yes, if you use too much glue it will be a giant mess when you push/twist - you'll learn as you go.
Yes, the glue is fine in the tank even if there's a ton extra. In my tank, coralline starts to grow over it a week or two after it turns solid.
I've accidentally glued a lot of things - coral polyps, fish mouths (this was the scariest by far), torch skeletons to their tentacles. Nothing has died yet! It generally cures and falls off within a few days.