Get a polishing cloth. (Other good subsitues are Brasso (with a
soft cloth), Windex and a soft paper towel (ex., Bounty) In addition to
a cloth, you could also use a product such as RadTech's Ice Creme.)
Rub the scratches on your iPod with it. Be sure to rub up and down
or side to side, never circular. If you rub circularly, it can make
scratches worse.
Tips
Be careful not to make the iPod scratches any worse than they already are.
Prevent further scratches, purchase a soft cover of some sort.
There are basically two varieties: the "wallet" and the stick-on
surface protector.
Warnings
Use care when working around iPod click wheels - avoid direct polishing/applying excessive pressure to this fragile mechanism.
Keep solutions away from the bottom of the iPod where the there are inputs/outputs.