For DIY you need to have some courage.
Contrary to popular belief scratches in hard materials can not be polished out.All that happens is you give the scratches a polished bottom but they are still there.
first you need to get rid of the scratches - this requires using a course abrasive and then successively finer grades of abrasive until the scratches are reduced to just a smooth matt finish.
This can then be polished out. for glass you need to use professional polishing materials and possibly a powered polishing mop until the surface is once more shiny.
A you can see this is time consuming and requires quite a lot of equipment.
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rick' is right on this one L
"on this one" - I am hurt!!! :-)
Sorry man, I meant to say "rick' is right, on this one question you've got your answer already." but I fouled-up the typing....... : ) L
:-) only pulling your leg (metaphorically speaking that is)
I know, I was going with it. L
Suggestion: Ask a glass store to give you a quote on a replacement table top. Price depends on the size, thickness, and complexity of the shape -- and whether you need the edges polished for safety, and whether it needs to be safety glass (if the glass is resting on something, maybe not; if the glass _is_ the tabletop, it probably should be). Depending on what you're dealing with, it may be more affordable than you'd think.They may also be able to give you a quote on polishing, or advise you on whether it's worth trying a wax/varnish to soften the edges of the scratches and make them less obvious.Depending on what you're dealing with, simply turning the tabletop upside down so the scratches are on the bottom might be an improvement...
Try rubbing oil over them. It makes them much less visible.