One way is to load your bag with different colors, use a spatula and place the different colors along the sides of the bag. You can take straight color and brush it on the sides of the bag. You can also use icing "bullets" and place different colors in the same bag. I have only ever used two colors when using the first and third methods, not sure how many colors you can get at one time. I just googled "icing bullets cake central" to show you what an icing bullet was and this was the first (of many) links that showed up. http://cakecentral.com/cake-decorating-ftopict-743677.html/
AI know that it has been a while but, I thought that I would share how I did my rainbow effect. I had purple, pink, red, yellow, blue, green, and white buttercream. I put all the colors in piping bags then I did a line of each color up the side of another bag. I put white in the middle of all the colors, white is needed to keep the colors from blending together and making unflattering colors. I don't have pictures, but it came out so pretty.
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