There are a few different methods to achieve this. The end goal is to get layers of different colored frosting in rings in your piping bag. The method I ended up preferring uses a piece of cling film/plastic wrap along with your piping bag and tip. This method also makes it easy to have colors change as you progress.
Start by cutting off a square piece of cling film (about 12"x12" or 12"x15"). In the center of it, either pipe or spread a 1/2 inch thick layer of the color you want to appear on the outside in a rectangle about 4 inches wide and 9-10 inches long (be sure to leave an inch or two on either end of the rectangle. On top of that, make a narrower rectangle with your second color but going the full length of the first. Finally, put a very narrow rectangle or strip of the center color on top of that.
It should end up looking something like this:
At this point, carefully roll the three layers into a cylinder, making sure the ends of the largest rectangle meet completely. Twist the cylinder ends to close them and prepare your piping bag with the tip you want to use. Trim one end of the cling wrap and feed that end into the piping bag. Twist the end of the piping bag to close and you should be ready to start piping!
Part of why I like this method is that it's pretty simple to let your colors drift to change what the primary (outermost) color is by adjusting how you lay out the colors. So, if you want four colors and you want the outermost color to change from darkest to second darkest and the innermost color to also lighten from the third to fourth color, you could lay it out like this, instead:
In this case, the darkest blue stops where the second one is the full width of the frosting rectangle. I used the same shades of color in this example but you could use any collection of colors you want. As you pipe, it will muddy a bit but, all in all, it's pretty effective.
Different thicknesses of frosting layers and widths of bands will change which color predominates. A thin outermost layer with a thicker, wider middle layer will tend towards tips of the outer color with a predominance of the middle layer.