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There are a variety of tools available online and at electronics retailers. One of the most popular products is the SkipDr, though there are several others available as well. Use warm water to rinse any debris and dust off of the disc, then dry it off with a microfiber cloth. Most repair kits come with a soft cloth you can use. Don't spray it onto the label. Apply an even coat across the entire "read" side of the disc. The process for this will vary depending on the tool you are using. Make sure the "read" side is facing the scrubbing pad on the repair tool. Refer to the instructions to make sure you are inserting the disc properly. You may need to turn a crank or press a button to make the disc spin. The repair tool will spin the disc, rubbing the cleaning pad across the "read" side. {{greenbox: Note: You'll likely need to spin it several times in order to buff out scratches. Many repair kits come with a buffing cloth, which you'll use to buff the disc after repairing it. Vigorous buffing will help ensure that the disc can be read. use the cloth and buff in small, concentric circles around the read surface. Insert the repaired disc into your Xbox console and try playing it. If it still doesn't work, you can repeat the repair process again. Some users have reported it taking up to ten tries to get a game to work. Some scratches may be too deep to repair using these tools.

Summary:
Purchase a disc scratch repair tool. Rinse and dry the disc before using the disc repair tool. Spray the included cleaner fluid onto the "read" side of the disc. Insert the disc into the repair tool. Press the mechanism to spin the disc in the repair tool. Buff the disc with the included buffing cloth. Try the disc.