Coloring the frosting is very simple if you have high quality food colorings to work with. Those little bottles of food coloring you can buy in the spice isle of the grocery store have their place, but it's not in cookie decorating! The colors are watered down so much that it's impossible to get the vibrant colors you are looking for. The soft gel paste colors that I use are very concentrated, and one drop goes a long way. Investing in some good colors are worth it in the long run, since they last so much longer.
Here are a few general tips for coloring:
Make up more of each color than you think you'll need. It's very hard to match the color exactly again if you run out, and it will just tack on more time to your project if you have to go back and make more.
Make up all of the colors you will need at the same time. I start with the lightest color first so that I can use the same bowl for all of my colors. For example, lets say I need yellow, green, blue, and purple for a specific design. I will start with the yellow. I color what I need and put it all in a decorating bag (click here for information on preparing the decorating bags) scraping as much as possible out of the bowl with a rubber spatula. Then I would move onto the green, by scooping some plain frosting into the bowl (which now has traces of yellow frosting left), and mix up the green, continuing on as before, on to the blue and then to the purple. There are several bonuses to this trick. First is fewer dishes, which is a huge plus, and the second bonus is that your colors will actually match each other better if you combine them a bit. If you've ever taken a painting class you may have heard your teacher say not to use paint straight out of a tube (you should mix it with another color first). It's the same thing with food coloring. Your colors will actually work better together if you do this.
Remember that your frosting will actually get darker as it sits, especially red and black. Don't add so much color that it looks very dark right away because it will get even darker as it sits in the bag or bowl. A good thing to do (if you have the time) is to make up your colors the night before and let them sit overnight. If they still don't look dark enough in the morning you could always add more color. It's easier to add more color than it is to take it out! If you need to save a bowl of frosting that is too dark, add some white frosting to tone down the color.