[edit] Steps

Determine what kind of painted surface you have. If it's the interior of a house then you can be pretty sure that it's latex paint. A product called "Goof Off" is available in home stores (paint department). There are some citrus-based solvents available too, generally in the same area.
Scrape what you can of the tape off with a fingernail or a putty knife, being careful not to scratch the painted surface. A nylon pancake spatula might work too. You have to try to get the paper part off first so that the solvent can work on the glue.
The Goof-Off is going to dissolve both the adhesive and the paint, so work carefully. Put a little on a rag, rub it on the adhesive just until it's removed. Then wipe off the remaining solvent with another clean rag or paper towel.