Make sure you have newspaper or something to protect the table so you don't have a mess.
Once you get a big mound of bubbles, lay the paper on the bubbles. The bubble pattern will transfer onto the paper. Some of the smaller bubbles will stick to the paper, and that's okay. They will pop and leave a slightly darker color spot. Repeat this process until you have covered the entire paper. You can use several different colors on one paper. The end product will look something like this.
The colors didn't turn out very bright in this picture, but it looks better in real life. Once these creations dry, you can cut out shapes and glue them onto construction paper, or use them in all kinds of paper crafts (scrapbooking, card making, etc.). They're a lot of fun to make, especially the blowing bubbles part.
Here is my expert bubble artist at work.
Notice the newspaper protecting the table top.
Let me stress again the importance of blowing OUT, not sucking IN. I did this craft at church with a group of 3-5 year olds. One little boy didn't listen to the instructions. When he got his paint/water/soap mixture, he promptly took a big drink and got a big mouthful of soapy water. The poor kid probably cried for ten minutes and refused to complete his project.