I first got the idea from this site. Instead of dyeing regular paper, I dyed envelopes.
lots of paper towels
skewer (or something to stir with)
foam brush (optional – just for smoothening out the foam)
1. Spray some shaving cream into pan and spread it evenly onto the pan. Go easy, that stuff spreads a lot.
2. Put a couple drops of food coloring, whatever colors you'd like to use.
3. Stir the food coloring around some. I found that going in circles one direction works well for some really good designs. Also, don't over do the stirring, the swirls will not be as defined.
4. Put the envelope onto the foam and gently tap down so the foam/color hits a lot of the envelope.
5. Remove the envelope from the foam and blot the shaving cream off. Don't worry if you don't see the swirls when you first pick up the envelope from the foam. Once you blot, you should see the design. I've tried to wipe it down, and it smears the color – so I wouldn't suggest it. Blotting seems to work the best. Did I mention that you'll be using a lot of paper towels?
6. Once you got the shaving cream off, you just need to let it dry.
As an added bonus, the paper feels smooth and smells pretty good at the end of it all.