To polish a blade you usually finish it with a cloth or felt wheel on a motor. It's called a buffer. The wheel is coated with an abrasive paste called tripoli, that comes in small blocks of waxy substance. The heat of the attrition against the wheel melts the wax and makes the abrasive stick to the wheel.
The buffer can polish a blade to mirror shine. Is also a very dangerous piece of equipment. Wire or pieces of cloth can snag in the blade, rip it from your hands and throw it with incredible force. For this reason you must always use the buffer with the wheel turning down, and the blade positioned so that if it snags, it is thrown away from you.
Another method is hand polishing. Longer, but safer.
The other crytical factor in getting a mirror surface is the type of steel you are polishing. Powder stainless steels are those that get the best polish. Standard carbon steel won't get such a mirror polish and is best left at a 600-800 grit satin finish, possibly lengthwise.