The Disk Doctor does a pretty good job, but failing that, don't waste lots of money buying dedicated scratch removing polishes. Buy a can of T-Cut or similar abrasive car colour restorer and use this for deep scratches, always rubbing at 90 degrees to the centre hubring, in other words, from the outer edge to the inner hole, using even pressure, and don't just do where the scratch is. Do the whole disk to keep the surface as even as possible. Use a small piece of smooth wood, about two inches long, half inch thick and one inch wide wrapped in a piece of strong cotton cloth/linen and keep the disk flat on a very flat surface such as a kitchen worktop.
Light scratches can be removed/improved using Brasso or similar, an extremly fine abrasive metal cleaner. Use in the same manner as above.