Paper marbling is basically a mono-printmaking process. We found that a few key things severely hindered our previous attempts: not coating our papers with Alum prior to marbling; not using the right paints, diluted to the right consistency (this time we used Marble Art paints and Golden FLUID acrylics, further diluted and we did not mix these two paints together); and not using carrageenan in the water tray, which creates a surface on which the paint can float. (We previously used methyl cellulose or wallpaper paste, which some paper marblers do use).
John recommended a few great resources for information and supplies: The books, "Ultimate Marbling Handbook" and Galen Berry's "The Art of Marbling" which can be found on his website: Marbleartus, (which is full of help and supplies you can order to get started.) Check out Payhembury Marbled Papers and Falkiners for gorgeous examples of hand-marbled papers and other resources as well.
Below is Galen Berry's brief description of the process, taken from his website. I have added some photos from our day and a few italicized notes.
1. Some alum is dissolved in water. This is sponged onto each paper to be marbled, and the paper is allowed to dry. The alum is what will bond the color to the paper.
2. A thick liquid, referred to as the size, is made by blending a type of gelatin (carrageenan) with water.
3. The size is poured into a shallow tray. (We used these disposable trays but something with more square corners would be even more effective.)
4. Several colors of ink or paint are sprinkled onto the surface of the size. They float on the surface because they are lighter than the thickened water. (We used the spatter method of applying the paint to the water but you can use a brush tip or dropper to form more distinct and even patterns of color.)
5. A stick is used to stir the floating colors if desired. Various combs and rakes may also be run through the colors to make more intricate patterns.
6. A sheet of the alum-treated paper is gently laid onto the surface of the size, and it absorbs the floating colors. Only one print can be made.
7. The paper is lifted off, rinsed, and hung up to dry. (The image, above right is a wet sheet just pulled from the tray, before rinsing. You will notice some white spots, some of which are reflection from the camera flash on wet paper. Some white spots are caused by air bubbles trapped between the paper and the surface of the water.) Fabric marbling is done the same way, except for step #1: Instead of sponging the alum onto the cloth, it is soaked in the alum water, then hung up to dry, then ironed flat. After that, it can be marbled just like a sheet of paper.