Polish your bowling ball. Any bowling alley shop can sell you polish and abralon pads. Put a small amount of polish onto the surface of the ball, and then rub it around the surface with your fingers. Rub the ball with the pad to remove scuffs on the surface. If the ball is very dirty or has scuff marks, you might need use a cleaner specially formulated to remove oils and ground-in dirt.
Sand the surface of your bowling ball to remove nicks and scratches. The level of grit the sandpaper depends on the effect you want your bowling ball to have in the end. For example, if you hook the ball with each shot, lower grit will work better when sanding the surface.
Try an "insta-patch" kit sold by pro shops and online. These aren't recommended for large imperfections, but you can repair small gouges and nicks by filling them with resin and then sanding and polishing the area to make sure it's smooth.
Resurface the ball to fix any other warping you notice. Invest in a home ball spinner if you bowl frequently enough to justify shelling out a few hundred bucks. Place the ball into the spinner and follow the instructions included with your specific spinner. Alternatively, take your bowl to a pro shop to have it resurfaced. You do not need to perform this task too frequently; once after every 30 or 40 games will suffice.