The clear nail polish method involves a starvation of air flow, as does the duct tape method. (In fact, a 2009 study quoted in the National Institute of Health seemed to use a version of the duct tape method, calling the device “a flat adhesive patch”.) In these cases, 3-6 days is often recommended for application, until the skin tag breaks contact with surrounding skin. Of course, this would be problematic in areas not seen by the public.
A faster method, used in medical facilities, can be to sterilize your own scissors (in boiling water or alcohol) and snip the skin tag directly. Preparation can be taken to reduce pain by holding an ice pack over the skin tag for 20-30 minutes beforehand, and having bandages nearby for possible blood flow.
Since little is known about the origins of skin tags, it’s difficult even for the medical community to reach a consensus on effective home treatments. Of course, the surest sign of removal is when the skin tag falls off. (This can sometimes happen whether or not any remedy is tried.) However, Medicine.Net does say that there are no officially approved creams, and over-the-counter wart removers are not considered effective any more than nail polish or oils.