You need procion reactive dyes. Rit (the stuff from the supermarket, all they ever seem to have) really sucks donkey balls. AC Moore and other craft stores have tie dye kits that will get you started. Naturally, the net is a great place to find procion dye suppliers.

You only need three colors: fuschia, turquoise, and yellow. Combining these colors will provide a nice gamut.

Make sure you first treat the fabric with a solution of sodium carbonate (NOT Baking Soda, which is sodium bicarbonate, and is not basic enough). Let it soak in a solution of 1 cup carbonate per gallon water for at least an hour. This soaking will activate the fabric toward reacting with the dye. Wring out the fabric thoroughly (use gloves, the pH of this solution is about 14, and will burn your skin).

For the typical spiral rainbow pattern tie dye:
Flatten the fabric onto a plastic garbage bag. Place a 1/4" dowel (or a pencil) on the fabric where you want the pattern to be centered. Holding the dowel firmly into the fabric, turn it. This will start to spiral the cloth, with many folds, around the dowel. Continue to turn it until the fabric forms a tight bundle. While the dowel is still in place, place three rubber bands around the fabric, separating the pleated surface into 60 degree quadrants (just like a Trivial Pursuit piece carrier). These rubber bands will hold the bundle together, and act as guides for dyeing the fabric. Remove dowel. Cover half the fabric with each of the three (fuschia, yellow, and turquoise) dye colors. These halves overlap each other, only mixing with ONE of the other colors in a quadrant (e.g. the yellow half will have a quadrant in which it mixes with fuschia, a quadrant (in the middle of its half) that is yellow by itself, and a quadrant in which it mixes with turquoise). Be careful around the center 1/2" or so. Only fill it with one or two of the colors, or it will turn to brown mud.

Let the fabric stand for a day. After a day, rinse thoroughly with cold water. Wash by itself. You may now wear it. The following diagram may help visualizing how to apply the dye to the bundle:

                     /----             ----\
                  X//                       \\\
                // \         fuschia          X\
              //    \\                       //  \\
            //        \\                   //      \\
           |/           \                //         \|
          ||  fuschia    \\             /   fuschia  ||
          |      +         \          //       +      |
         |    turquoise     \\      //      yellow     |
         |                    \   //                   |
         |                    // \\                    |
         |    turquoise     //     \                   |
          |               //        \\    yellow      |
          ||             /            \              ||
           |\          //              \\           /|
            \\       //     turquoise    \\        //
              \\   //           +          \     //
                \X/         yellow          \\ //
                  \\\                       ///
                     \----             ----/