It's easy as coloring with crayons or painting with a brush, before you embroider.

Fabric Paint
Any fabric paint would work, I like Ready-Tex Fabric Paint

Iron freezer paper to fabric back.
Transfer design
Shake paint well and use a regular paint brush to test on a scrap of fabric first.
Color lightly first then go over again darkening and hiding any uneven coloring.
Allow paint to dry before painting another color.
When paint is dry, embroider using two or three strands of floss in a darker shade than the paint.
Follow instructions for paint if it needs to be heat set.  Ready-Tex is heat set for two minutes, using a cloth or paper towel on top.

 For a bold color use paint full strength, some colors may feel stiff; you can mix with water for a softer feel.

 For soft color, looks like crayon, wipe off excess paint on a scrap of fabric or paper towel before painting.

Color Crayon Method
Color does tend to lighten after washing

Iron freezer paper to the back side of the fabric.
Transfer your embroidery design to the front.
Color the design with regular color crayons, First color lightly then go over again darkening and hiding any uneven coloring. 
When finished remove the freezer paper and embroider using two or three strands of floss in a darker shade than the coloring.
When embroidery is done, lay face down on the shiny side of the freezer paper and iron the back side, for about 30 seconds
(this sets the wax onto the fabric).