Work the fabric around the snag with your fingers to ease some of the pulled thread back into the fabric weave. Pull the fabric lengthwise along the snag, and width-wise to either side of the snag.
Insert the snag repair needle into the upholstery, 1/2-inch away from the snag. Bring the point back out at the base of the snagged thread.
Twirl the snag repair needle around the snagged thread to secure it, then gently pull the needle back through the upholstery so that it drags the loose thread under the surface.
Snip the end of the thread if it reappears through the exit hole as you remove the snag repair needle.
Add a tiny spot of fray check to the area where the snag was, if the snag made a hole. If there is no hole, leave the fray check off.