Thread your curved needle and put a knot at one end of the thread. Using a curved needle is imperative to get a smooth stitch. It will come up from under the felt on its own.
Start at one end of the tear in the felt and push the needle down through the felt on one side of the tear. Push the needle through up through the other side of the tear. Make sure to ply your needle about half an inch from the tear on either side.
Pull the thread tight and make another stitch in the same way as above. Continue along the length of the tear, pulling the thread tight between each stitch.
Knot the thread when you reach the end of the tear and trim off the excess thread from both ends.
Rub a pool ball over the stitches to help smooth them and press them flat. Press hard against the pool table.
Heat an iron and run it lightly over the stitches in the pool table felt. Roll a ball over the stitches and watch to see whether the ball veers off course when it goes over the stitches. If it does, iron it again. Continue this process until the stitches do not affect the ball's trajectory at all.