1. Wash the area were the scratches are at.
2. Use a clay bar to remove micro contaminants in the clear coat.
3. If the scratches are that deep use heavy duty compound to polish the scratches.
4. Then finish it off with a fine finishing polish.
I recommend that you use a buffer to do this since using your hand will probably not bring the best results. If you must use your hand

, then use a foam applicator pad to apply the compound and polish.
If the scratches are reallly really deep, you'll need to take it to a professional and have them wetsand the scratch and compound and polish it. If you can feel the scratch with your finger nail, nothing you do will completely bring it out, only it will lighten up.