Rubbing Alcohol
In order to use the rubbing alcohol method you need to first clean the lens with a microfiber cloth and a bit of lens cleaning solution --- make sure you don't apply the lens cleaning solution directly to the lens. Next, dilute a solution of rubbing alcohol and water, with 1 part alcohol to 20 parts water. Dip a new microfiber cloth into the solution and gently rub the cloth into the scratch. If this method works, the scratch will begin to visibly diminish. Continue rubbing until the issue is resolved.
Scratch Repair Kits
There are many different types of scratch repair kits you can purchase to help resolve a scratch on a lens. You can find a scratch repair kit at a photography lab or a photography supply store. Because so many options exist, be sure to purchase a kit that matches your camera and lens type -- you could risk making the problem worse if you use the wrong product. Follow the manufacturer instructions on the kit to repair the scratch.
Petroleum Jelly
You can also use petroleum jelly to help remove scratches from a lens. To use this method, clean the lens with a microfiber cloth and lens cleaning solution and then let the lens dry off. Apply a small amount of petroleum jelly to your finger and rub it into the scratch, filling the entire scratch. Wipe the jelly off using a new microfiber cloth --- be careful not to press the jelly into the scratch. The petroleum jelly will create a protective coating that diminishes the appearance of the scratch. If this method works for your scratch, be prepared to re-apply the jelly, as it will fade.
Eraser
As with most scratch removal techniques, you must first clean the lens with a microfiber cloth and lens cleaning solution and then let the lens dry. Use a clean unused eraser and gently rub the surface of the scratch. The eraser removes small surface scratches by gently smoothing them out. Rub off the eraser bits and re-clean the lens once you have used this technique.