The above video is a carefully designed step-by-step tutorial on how to marble your nails. Now, I've watched many of these tutorials and have found this particular one simple enough and thorough enough to give you confidence to try it yourself.
There are several key ideas the narrator introduces that make this tutorial an excellent introduction. First she stresses the need to use scotch tape around your nails to minimize clean-up of excess polish that is inevitable, given the process. There's nothing worse when polishing your nails than to have oodles of polish left on your skin after the process is finished. Not only is it bad for your skin, but it's difficult to remove the excess without disturbing the polish you want to remain there on the nail itself.
Second, she emphasizes that you need to use new nail polish as polish that has been sitting around for a while tends to thicken and will not swirl as well on the surface of the water.
Third, she suggests that you begin and end with clear nail polish in order to protect your nails and to give the final product an attractive sheen. She also recommends covering that first application of clear polish with a couple of coats of white polish as a background on which the colors will really stand out.
If you only watch one of the videos I have posted on this wizzle, watch this one.