You can use sandpaper exactly like you would use a stone. You can go edge first, edge trailing, circular, whatever you please. Even on soft backing, I have not cut into the sandpaper when going edge first. Definetly not a problem on a hard backing.
Sandpaper is great because you can cheaply acquire a large array of grits, that would be insanely expensive to buy if you had to get a stone for each different one.
Bo T has a point about the carbide hardness on steels like S30V. In theory the sandpaper (usually aluminum oxide or silicon carbide) is much harder than the steel matrix, but slightly less or roughly equal to the hardness of the vanadium carbides interspersed throughout the steel. So it will abrade the steel down to an edge, but the little chunks of carbide at the edge cannot be worn down by the sandpaper- they either get knocked out by the force of sharpening, leaving a jagged edge on a microscopic level, or remain there sticking out from the edge. You would need diamond abrasives to wear down the carbides reliably. This is not just an issue with sandpaper, but all abrasives which are not diamond.
However, in practice I don't find this to be an issue. I do have course diamond hones, but I use either sandpaper or waterstones for the higher grits. I can get S30V just as sharp, with as high of a polish, as my other steels. Which means cleanly pushcutting phonebook paper, hair popping sharp. Perhaps you would have trouble achieving absolute perfection with sandpaper, but you can get it plenty sharp. Besides, the carbides on a very fine S30V edge are not too stable, and tend to cause the edge to become toothy rather quickly. It will then hold that toothy edge a long, long time. So, it is not so productive to put that perfect hair splitting edge on. What you get with sandpaper should be fine.
