If you want the dirt cheap method that also works well, especially on 3-blades, just get some wet/dry sandpaper from an auto parts store. Depending on how dull the blades are and whether the edge angle needs to be adjusted, you can start with 220 or 400. Then go to 600 for a really nice edge and if you want a real mirror finish, use some 1000 or 2000 grit.
I lay it flat on a piece of glass, spray it with some water, hold the top of the paper down and pull toward me. Or, hold the bottom down and push away from you. You want to be dragging the head from heel to point so you don't slice into the paper.
There's a slick "how to" on here showing a board with a groove in the end and using a clip to hold the paper.
Anyway, you can go as coarse as needed to start with and as fine as you want (I've seen 6000 grit). It's not necessary to go finer than 600, though, to get a nice polished edge with no visible scratches.