I have painted the trim with semi-gloss latex paint. How long does it need to dry before I can mask it with blue painter's tape?
We try wait at least 12 hours and use Orange core tape (delicate, low tact) and often we still get a little pull off. Don't leave the tape on any longer than you have to and pull it at an extreme angle to the wall or trim. Obviously, the longer you can wait to tape over fresh paint the better, but we don't have a lot of time on a job to wait for the paint to cure. Trim paints tend to pull off more than wall paints, so we break the common rules and do walls first, trim second. Also, small touch ups on egg shell or flat wall paint is easier than touch-ups on semi-gloss trim.
In hot humid weather and rush jobs, we use fans and dehumidifiers to speed the curing process. This helps a lot. Under optimal conditions, we can tape after maybe 4 hours and do second coats in the same day.
Side note: Use only good grade paints with proper prep. Cheap paint will peel off with your tape even after days of drying.