I have large glass table and it's acquired some scratches over time.
How can I remove or soften scratches on my glass table top?
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This is an old question, but there are some points missing from the other answers that really need to be stated...
First, I would recommend you not even try. The reason is that most glass tabletops are made of tempered glass. The tempering process creates internal stresses within the glass sheet, so that if it breaks it will do so along those stress lines. This is a safety feature1, but it comes with some drawbacks: any cutting or polishing must be done before the glass is tempered. If you cut tempered glass, the whole sheet will shatter, almost 100% guaranteed. Trying to polish it is not quite as risky, but there is still a very high probability of breaking it. All it takes is a slight change in the internal stressing forces, and the whole sheet falls apart.
If you absolutely must try this, get a product with Cerium Oxide, and be willing to settle for an improvement instead of chasing perfection.
1: tempered glass breaks into small chunks that are about the size of a fingertip. On the other hand, non-tempered glass breaks however it wants, which is usually into several large shards with long edges that are sharper than a Feather razor. Large pieces of non-tempered glass are incredibly dangerous if they break.
There are commercially available glass polish products that can be helpful and this is an example:
Get such a product and follow the manufacturer's instructions for use. Keep in mind that polishing scratches can take considerable time since you must remove quite a bit of material over a reasonably large area to get the scratch out.
There are also some products that claim to be able to fill scratches in glass but I've not had any success with any of them.