This is not an easy process and you can go about it in a lot of different ways. Some folks employ the "old" standby Marshall Oils which are specially made for painting on photographic surfaces. But you can also employ many other devices from a highlighter to colored pencils and watercolor paints.
Because I do not often create a hand-painted piece where the colors are the central focus of the image (although one might argue that they become the central focus as a result of the painting or coloring process), I most often will print to a watercolor paper that allows me maximum flexibility in the coloring process.
One caveat I would quickly add is that if the sharpness of the image is important to the final product, this is NOT the approach you will want to take. Watercolor paper, by virtue of the uneven nature of the paper will not yield a crisp reproduction. If you want that you will need a paper more specifically produced for photographic purposes. Watercolor paper yields a more ethereal image.
The image to the right, above, entitled "Buffalo Road Horses #82" is the original image with which I started. The image went through several iterations on my desktop before I printed the black and white image from which the final Mindscape was created. In the case of this image, I used watercolors to achieve the final product - sometimes I will also combine colored pencils where very fine coloration is required but that was not the case in this image.
The final image "Buffalo Horses Mindscape" is a far more ethereal view of the scene from which it came.