Select a sewing needle suitable for your upholstery. Use a long sewing needle, with a width that easily moves through the fabric without breaking any fibers. If the needle is too thick it will punch a hole in the fabric, and if it is too thin it will be difficult to push through the upholstery.
Push one end of the thread through the eye of the needle. Pull the thread through the eye, so that you have an equal amount of thread on each side of the eye.
Insert the tip of the needle into the upholstery, next to the snag. Place the needle tip as close to the snag as possible.
Push the needle through the upholstery and back up and out of the upholstery. Work slowly.
Wrap the snag around the thread, as you pull the needle through the fabric. The object is for the snag to hitch a ride with the thread on the needle, so that you can pull the snag to the opposite side of the fabric and out of sight.
Pull the needle all the way out of the upholstery. If done correctly, the snag will disappear to the backside of the fabric.