All you need are two different polishes - I used Essie 'Cute as a Button' as the base color and Sephora by OPI 'Only Gold for Me' topcoat for the triangles/chevrons.
First, I painted my nails as I normally would, and finished with a top coat. After I was certain that they were dry, I applied tape to my nails to create the shapes.
After securing the edges of the tape, paint over your nails with the top color of your choice, and then the tricky part is peeling the tape off. It creates a little bit of a sticky layer where the polish meets the tape edge, so you want to make sure that you let the top color dry a little bit, and then use another layer of your clear topcoat after you've peeled the tape off. Viola!