I give it plenty of time to dry then give it a light wipe with a slightly damp rag. I've found that there is some residue that comes off with the first coat of oil but not enough to affect the final colour.
If you are doing a blue colour, DO NOT use Tru Oil!!! It will yellow over time and turn your lovely blue to a crappy green. Happened with my Tele. Use an acrylic clear coat.