There are many ways of working with color on the peg loom.
One is to work intuitively, adding and changing colors whenever, wherever you want to.
Another, is to use a cartoon or template- a technique that I cover in my book: Peg Looms & Weaving Sticks
If you would like to chart out designs and work from them, I have made a video showing how I worked from this chart:
In the video, I show how to work a locked join when changing colors, as well as simply stacking colors when working the diagonal lines.
Even though the techniques are shown on a peg loom, they work just the same on weaving sticks.
The loom in the video is from Dewberry Ridge Looms. The yarn is from Harrisville yarns.