Ah, tape and taping. Sometimes the bane of all things painting or the necessary step. I have to be honest and say that for me it can also be a mixed bag. Let's walk through a few things to help us with choosing the proper tape and taping. Otherwise, you may end up with an investment of time while receiving a dividend of anger and frustration.
The mantra for painting is this: clean, dry, and dull. Using tape on a surface requires 2 of the 3 previous adjectives: clean & dry. If you expect the tape to adhere to dusty baseboards or greasy cabinets, the tape and taping job will surely fail. Take a damp cloth and wipe down those dusty areas that you intend to tape and thoroughly wash any area that has a residue of grease, dirt, soap, or scum. You can wipe it, after washing, with a dry rag but still wait a few moments before applying the tape so that the remaining moisture has time to dissipate and not interfere with the tape's adhesive properties.
Tape selection is also a big part. Use masking tape for surfaces that can take the extra adhesive properties(like tile, formica, or wood) and knowing that the tape will be removed in rather short order and not be on the surface too long. I prefer to use the green FrogTape or the Multi-surface 3M Scotchblue for taping on most surfaces like cured paint, woodwork, or other semi-sensitive surfaces. I use the delicate surface tapes on freshly painted(at least 24-48 hours old) walls, on wallpaper, or very sensitive surfaces.
After you have cleaned the surface and picked the proper tape it is time to apply. Pay careful attention on how the tape's edge will be lined up with the edge/corner in which you want to protect. Gently press the tape to the surface and smooth it out. Be sure to apply some pressure to the tape when you are smoothing it out.
Your tape handy work revealed. Remove the tape soon after the job is done at a 45 degree angle against itself. If the tape is on too long the paint will dry and form a 'film' over the tape and painted surface which can cause the tape to pull paint from where you don't want it to - your nice paint job.