Some of the reasons people choose two colors for their walls is to create faux wainscoting, stenciling, stripes, faux marbling or borders. Whatever your reasons are, deciding which colors to use will depend a lot on the purpose of the space and existing color schemes.
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Decide on the design you'll be using. Whether it's stripes, stenciling, faux marbling or wainscoting, your color choices will have an impact. You might not want two bright colors side by side for striped walls, for example.
Choose colors you like that fit the function of your room. Color choices for a child's room will vary from a dining or living room space, for instance.
Try an online paint visualizer. You can choose a room style that resembles the one you'll be painting, and launch color visualizers to help you make your choices. Some will allow you to choose two colors at a time and see what they look like together. See "Resources" for a link.
Go to your neighborhood home improvement store and bring home several paint chips in your choice of color combinations. With masking tape, attach one pair of colors to the wall you'll be painting. Leave them up on the wall for a day or two. See how they respond to light during daylight hours and room lighting at night.
Repeat this process with the next set of colors. If you're leaning toward one set of colors, and if they work well together with the existing decor or lighting, these will be the right choice.