Open your Image. To show the procedure I picked an extremely simple image, to which I will add only a few colors
Add a New Layer and choose "Color" as its blending mode.
Pick a soft brush, select your desired color, then simply begin to paint over the area you want to color. If the color appears too intense, pick a color with less saturation. For large even areas (e.g. sky) you can even use selections. Repeat for other colors/areas. Generally speaking, tint variation is not necessary, as the luminance information from the underneath layer (that is, your original image) creates the adjustment required. Of course, feel free to experiment. As I said, the more time you spend on it, the better it will look.
When you are done, you may want to apply a Gaussian Blur with low values (e.g. 7-10) on the layer you colored, so that the transition appears even smoother.
It's really very simple. For simple shapes/surfaces such as this example, you need only a few minutes. More complex scenes will, of course, require more detailed work.