I'm using a stud finder with wire warning to determine where to mount a heavy shelf. I've located the studs but on one of those studs it also detects live power (which should be expected because there is an outlet on that stud and a switch on the stud to the left). Can I continue to drill into the stud to install the shelf? How can I ensure that I'm avoiding the wires? What precautions should I take to ensure safety?

Be sure you are centered on the stud and do not drill more than 1 3/4" deep from the surface.

I would remove receptacle cover and receptacle, feel inside box for mounting screws, that tell which side of stud it is, and if it is a 4" X 4" box, measure 2" from center of box to find edge of stud, mark that, then 1 1/2 inches over should be other edge, 3/4" from either side should be center, and other studs MAY be on 16' centers. If different size is found adjust accordingly. You may be able to tell with out removing receptacle with your locator.