Maguires scratch remover. I have done it by hand and by buffer. That's the cheap way to take care of it as long as it's not past your clear coat. If you want showroom new. Adams complete buff kit. That is the expensive route.
Meguiars scratchx 2.0 or meguiars ultimate compound will do the trick with a foam applicator pad. Bass pro shops have them from meguiars. U can get a 4 pk for like five bucks. Expensive yes...but they work.
My friends and family have used Scratch X quite a bit. Especially my dad and brother as they are very anal about their vehicles. I've used it a couple of times.
Use it just like wax. Our technique is that we rub it in very small circular motions. Then wipe off. Apply how ever much you think is needed. Don't rush it and don't do one long scratch all at once. If it's a deep scratch, it probably won't come all the way out, but it will look better. This stuff works pretty darn good.
I also use either a microfiber towel or cotton rag to apply this with as well. I don't recommend using a wheel of any kind, but whatever floats your boats.