There are a couple of different ways to add color to die cutting, one is simply to cut them out from colored cardstocks, the other is to add color yourself. You can use just about any medium you enjoy using like markers, watercolor, colored pencils, inking and more. This is a great way to add shading, shadowing, depth and dimension to your dies.
For this Halloween Witch Card Mindy die cut the witch and cauldron from white cardstock and used her OLO alcohol based markers to color them. She also used a stencil for the brick background and die cut an archway for the witch to peek out from.
You can find her complete video tutorial for creating this card over on the Hero Arts blog.