How can I edit the following texture...
...so it looks like this?
And how to create the burned spots
For cycles. Use the texture to control how two different shaders mix:
(the color ramp is just to control the the intensity of the mix, but curves or a color bright/contrast node would work as well)
A different option is to use the image to control the color on a single shader:
Or use the image to control the mix and create some displacement.
Or additionally use it as a bump map:
I didn't have a way to make a normal map on this computer, but that would finalize the effect, with some good lighting effects like your reference image.
You can use color curves in the node editor to change the color if you are using cycles. This can be found under the color menu. If this is meant for blender internal or BGE you should be able to edit the colors in the texture menu. I added some images to show.