Most computer stores should sell scratch repair fluids or kits, or will be able to do it for you. I'd definitely stay away from home repairs, because there's a good chance you could consolidate the damage. Failing that, try amazon - I entered 'dvd scratch remover' as my keywords in the search machine and
this,
this and
this popped up.
I've had considerable luck with just off-the-shelf wipes, but that was on a CD, not a DVD - DVDs tend to be more sensitive. My dad used to use a kind of fluid he could submerse the disk in, I know that much. I'm sorry I couldn't be of more help.
