Plastix works great on minor scuffs and lite scratches. I use a dremel with a soft cloth buffing wheel, takes some time but the results are always really good. You could use a rag or old sock and do the polishing by hand, but the dremel is much faster and easier on the arms.
Deep scratches require a bit more work, start with a fine grit sandpaper, say 1000, and work to a 3000 grit sandpaper, then finish with the Plastix. I would suggest practicing the sandpaper method on a scrap slab, one that is so bad you are need a reholder to fix it, or if you have the remains of a cracked slab.