My carbon frame only has clear coat paint and I touch up scratches with a small bottle of clear coat automotive paint. I've heard nail polish works too. If you have coloured paint then you'll have to find some that matches. Try a model shop, they have small bottles in lots of colours.
I usually just dab on some paint, but if you really want to get picky you'll need some wet and dry sandpaper, probably 1000 and 2000 grit. Start by lightly sanding the area and then painting and then wet sanding the paint after it's dry. Repeat painting and sanding if needed. If you want to spend lots of time you could get an almost perfect repair.