I have done a few...
First, find an image. I mostly use coloring pages that I either scan or download online.
Second, I use my graphics program (I use Paint Shop Pro, Photoshop would work too) to clean them up, and make them transparent (so it's just the black lines) and resize. If you don't have a graphics program, you can still make them, but when you print there may be little black marks in places you might not want because the scan wasn't very good.
Third, Print the image onto cardstock. This is your base. Sometimes I use white, sometimes I use the main color of the image. So if I was doing Pooh, I would print it out on Pooh's body color.
Fourth, do the rest of the layers. Since I am comfortable with my graphics program, I used the layer properties to make a different layer for each color I need. If you don't have an image program or aren't comfortable working with layers, you can just reprint the entire image for each color you need. If you are somewhere in between, you can temporarily crop an image to get just what you want. So for Pooh, you could crop down to just his head so you can print on white to make his eyes. Also, say for Pooh, even though I made his base the color of his body, I might print a second layer for his arms to give it dimension
Fifth, Cut all the little pieces out and then glue them onto the base.
Start with an easy character first, so you can see how everything goes together.
This is how I do it now, and I like it best. However, before I figured out how to do it on the computer, I used to print the image, and then use tracing paper to transfer the image to each color of cardstock. But it is sometimes difficult to get the little pieces to line up correctly, because there are variations each time you trace something, while with the computer everything is printed identical. I still use the tracing paper for black or other really dark cardstock. Printing on black, doesn't work to well. Also, when you do it this way there is another step...you have to draw in the definition lines. That is the part that always made me nervous. It's a lot of work to mess up when you are trying to draw lines on Mickey's gloves.