Swimming goggles are typically made from plastic. This makes them vulnerable to being scratched from the wear and tear of use in a pool over the course of time. To remove scratches that can foul the image you seen through the goggles, use an abrasive paste acquired from a hardware store or hobby store. The paste, while an anathema to glass and prescription lenses, is well suited to grinding down the plastic so that the scratch is removed. No specialised equipment is needed.
Wash the swim goggles with mild detergent and water, and rinse in a stream of water coming from the kitchen sink spigot. Dry the goggles with a soft cloth.
Lay a bath towel down on a table. Place the swim goggles on the towel with the scratched lens facing up.
Place a piece of waxed paper over the lens that is not scratched to protect it. Tape the waxed paper to the sides of the lens with strips of cellophane tape.
Apply a line of the abrasive paste from the tube along the length of the scratch.
Place an edge of the ultra fine-grit sandpaper against the lens, to one side of the scratch. Drag the edge across the scratch until it reaches the other side. Lift the sandpaper off the lens. Repeat this procedure two more times.
Hold the swim goggles and angle the lens that has the scratch so that you can see the scratch. If the scratch is still visible, repeat the entire paste and sandpaper procedure. If the scratch is no longer visible, remove the cellophane tape and dispose of it and the waxed paper in the trash.
Wash the swim goggles in the kitchen sink and dry them off again with the soft cloth.