Cut out the damaged piece. Use your razor blade and carefully cut out the damaged piece of felt. This doesn't have to be exact, and it's best if you can make it into a square cut. Pull up the piece you have just cut out.
Sand the area beneath the felt, and around the edges of the cut. Gently and lightly, use your 200 grit sand paper to smooth the area where the tear in the felt occurred.
Use the razor blade to cut the new piece of felt to fit. You may have to trim a little here and there, and this is mostly freehand work, so be careful and trim it just a little bit at a time.
Spread a tiny bit of contact cement over the space where the new piece is going to go. Take the old piece you have cut out, and use that to smooth the cement with. Make sure it is in every corner and along every side.
Put the new piece over the top of the cement and press it down firmly. If any edges overlap onto the original felt, they need to be trimmed with your razor blade.
Using a pool ball like a roller, go over the new piece of felt by rolling the ball over the area several times. You want the edges to be nearly invisible and the join to be perfectly smooth.
Allow the table to dry overnight. Within about 24 hours, you should be ready to play some pool.