When you're planning how to mask what you're working on, try to leave yourself a corner or whatever that you can hold on to when you're done painting to remove the mask. Not always possible I know but...The reason I suggest that is you want to remove the mask/tape as soon as you can after painting. Once the paint dries it will tear or lift when you try to pull the tape off. Try to remove it when the paint gets tacky. When you're pulling off the tape, peel it back at a low angle and slightly away from the edge of your painted surface.
Some folks also use Bare Metal Foil for masking and say that it works very well but for anything other than small areas, it would get expensive in a hurry.
I don't like the blue painters tape because it doesn't want to stick to itself so overlapping pieces of it doesn't work well. At least not for me.
Something that may help with the edges is to lay out a strip of tape on a mirror or piece of glass and trim it with a sharp hobby blade or razor blade and a straight edge. It's also an easy way to make thinner strips for small areas or parts out of a wider tape. And it removes some of the tackiness also.
I recently got some of the Tamiya tape but haven't tried it yet. Also, got some liquid masking agent for the tight spots it's hard to get tape into but haven't gotten to try it yet either. I keep my tape in a clean sealed baggie when I'm not using it to help keep the fuzz and lint off the edges.