Is this vinyl siding that's textured or vinyl tiles that are glossy? If it's a glossy surface, I would first try to pick the old tape's residue with fresh one. Remove as much of the old tape as you can. Then apply fresh tape of same size or wider over the old and rub it in very well. Let is sit for a few minutes. Then pull the new tape off. Hopefully it'll pick up the residue of the old. If not all of it came off, bunch the removed new tape into a ball, sticky side out, and use that ball of tape to rub off the remainder of the residue.
If that didn't work or the surface has texture, you'll need to soften the glue with a solvent, then scrape it off with a spatula of rub it off with a rug. Alcohol, WD-40, charcoal grill starter liquid (it's 4th of July today, grill is on my mind :) ) as well as specialized products such as GooGone can all do the job. Just be careful with petroleum-based products such as WD-40 and grill starter liquid. They can leave oily stains on some surfaces. Try them in an inconspicuous corner first. I personally have a strong preference for using alcohol to eliminate a possibility of stains but WD-40 can be sprayed on, which is nice if you need to cover a large area.