Since I'm a silver smith, I have lots of jeweler's files lying around. I used a diamond grit file for this and just held the card firmly in one hand, with edges together and pushed the file diagonally along the edge of the card in short strokes. I like it so far.
This photo shows two cards, one on top of the other, one with a straight edge (bottom) and the other with a narrow distressed edge. I will probably widen that edge - to do that all you have to do is just keep applying the file, but angle it closer down toward the paper. Experiment on cheap cardstock first until you get the technique down. I think you could probably do it with a nail file or emery board, too - I'm going to try those next.
The photo below is of a card that's been stamped, had a narrow distress applied to the edge and then had the edge inked. I want a wider edge, so I will distress again and then re-ink, as distressing will remove the ink I've put on it.
Give it a try - let me know if you like it!
