I've used a microfibre cloth in the past, but I have no idea if this is the best way to do it. Works fine for me for metal and scratches around door handles.
I use cotton for aggressive work, along with cut up foam cutting pads. MF and (milder) foam for less aggressive work.
But what's *really* required is a lot of time and dedication And by "a lot of time" I don't mean just 15 minutes per area either. To speed things along, consider wetsanding with 4k first, but be careful about it.