Keep in mind that I started with a fairly low resolution photograph of my sketch for this tutorial, so the image is a bit pixely. This is the original image.
If your 'From Color' is not black, you can drag all the color setting dials to the left which will make it black. If the color you want to exchange is something else, use the color picker (Tools > Color Picker, then click on the part of your image that has the color you want to change from, which will send the color to the 'Foreground' box), then you can find out the RGB hex code (i.e. white is #ffffff). Enter the code into the color box on color exchange to select your color.
Next I started adding color to the bird and the background using the bucket fill, and zoomed in to ensure all the pixels were filled (or most, anyway - there were a few here and there I didn't bother with). I used these codes (#DE8371, #C33855, #D1CC56, #2E486B, #FFFFFF). I filled in the background with blue.
As for the colored branch image at the top of the post, I noticed some pixel shearing (I just made that up) along the top edge. I could go in and manually smooth it out, but I'll look for an easier way to do it.