There are lots of ways to tint your fabric for embroidery, with the most common being crayon tinting. In this post, you'll learn a few methods to try. With all of these versions of tinting, it's best to add the color before you start stitching. While it's possible to add the tinting after your embroidery is finished, it's much harder to color all the way up to the lines and without getting markings on your thread.
If you have a corner or turn that makes it really awkward not to change direction, you can either color using curved lines or color using very small circles instead of lines. Just keep in mind that how you color will always be visible and will create the appearance of texture.