The theory of chromatography is simple: you dab a dot of color onto a paper, stand the paper up in water, and let the rising water separate the colors by solubility. But how do you make sure the paper stays upright?
One easy method is to crease the chromatography paper vertically, then stand it in water. This works especially well if the bottom of the paper is cut flat (an angled bottom will make the paper tip.)
If the paper doesn't stand on its own, try folding the top of the paper over the side of the glass. Note that that this method is problematic: a professional biochemist cautioned me that surface tension between the glass and the paper might interfere with the capillary action causing the water to rise. However, it works well enough for M&M color separation, or the other basic chromatography we do in our kitchen. For better results, angle the bottom of the paper out so that the paper is not stuck to the glass.
If your chromatography paper is especially difficult to work with, clip it in place with clothespins or binder clips. Lay a pencil over the top of the glass and clip on the paper, forming a T with the paper hanging down, or take a shortcut and clip it to the side of the glass, as shown (angling the paper out from the glass, as above).
When doing chromatography with large groups, I use clothespins on a wire rack to suspend the chromatography papers over a dish of water. This way I only need one water container. (Make sure your scientists label their papers in pencil if they want to know which are theirs.)
Whatever chromatography method you use, make sure that the color dot is placed above the waterline. This is easy if you're hanging the paper--just hold the bottom edge in the water with the dot above the surface, then clip the paper in place. If you fold and stand your paper, make sure the dot is high enough so that it will still be dry when you stand up your paper. Then watch the water rise, and see what colors your dot is really made of.