Pull one side of the torn corner up as much as possible to reveal the carpet padding. Torn corners are ripped into two sections, and working with one side of the tear at a time is easiest.
Apply carpet adhesive to the carpet backing on the side of the tear you are holding. Be careful not to get it on the carpet pile.
Tug the side hard toward the corner, and press it firmly into the carpet padding.
Repeat the process with the other side of the tear.
Press both hard, and let them sit for several hours until the carpet adhesive cures completely.
Roll a carpet tractor over the area to blend the carpet fibers with each other again. This helps hide the torn section.