If I wanted to create different shades using Food Coloring, is there a different method of mixing them or would the same principles apply as with paint. Is there a standard mixing chart that details the different variations that would break down the process?
Yes, the principles are the same as for paint. It is subtractive color, meaning each new color you use subtracts out all of the colors except the ones it reflects. The other kind is additive color, when you are mixing lights like on a stage or out of a television set, and doesn't have much application to food that I can think of.
It's a pigment, so the principles are the same, but there's a few caveats when you're dealing with icing (and other than making fake blood, or dying cookie dough to make pie chart looking cookies, it's the only time I've ever died food for no other reason than to be decorative)
Liquid colors will throw off the consistency of icing if used in any large amounts. Powdered colors (available at cake supply stores) don't fully encorporate right away, and will be a deeper color the next day. Gel colors (available at cake supply stores, and at large craft stores, such as Michaels and AC Moore) are available in more colors, which makes it easier to match colors.
You can also get white powder for lightening shades. (it takes a lot of icing to try to turn red to pink ... you're better off taking a new batch of white, and add a little of the over-dyed icing to it 'til you get the right shade) .. or using pink gel color to start with. White can also be used in non-icing applications to try to lighten things.