Put a bit of the baking soda paste onto a wet cloth,and wipe onto the scratches of the glasses with small, circular rotations.Then put the glasses under the running water to remove the baking soda paste and clean them with a soft, lint-free cloth. If the scratches remain there,repeat the process above till they are gone.
You mean you want to remove scratches from the lenses. There are so many ways. But I suggest you to ask help from an optician if your glasses are very expensive, he or she can do this for you. They are more professional in doing this. Maybe they will charge you. But that won't be high. Good luck!
There is a kind of solution which can help remove scratches on the lenses. But if they are a pair of computer glasses, the coating that can help block computer reflections and glare will be removed too. And you can't get your glasses recoated.
You can use the cleanser that helps to clean the helmet of a motorcycle. I had a try on my sunglasses. It works. You can put some cleaner on the lenses and then rub your lenses with a piece of clean cloth gently. Repeat this for several times. You will remove some mild scratches. As to the deep scratches, I think they can't be removed easily. This way is just suitable for mild scratches. Have a try!
My mum has a pair of scratched reading glasses. There are so many deep scratches on the lenses. Once I suggested her to throw them away and bought a pair of new reading glasses. She said that she seldom used them so she didn't need to buy a pair of new reading glasses. But I think she is not right. The scratched glasses will blur our vision and we can't see things clearly. This may lead to eye strain. If the scratches on your glasses are also very deep, they can't be removed. I suggest you to throw them away and buy a pair of new glasses. You can buy a pair of glasses online because the glasses sold online are much cheaper than that in local eyeglasses stores.