"How can I make her hair color black with Photoshop?"
For a better reading experience, I would recommend visiting to Quora for my original answer.
Disclaimer: Okay, so normally this would be a simpler process, but there were quite a bit of noise and artifacts in the original picture due to the low resolution so I had to take a few steps to normalize the end result. I’ll tell you about them in a bit.
Typically, this should be a pretty straightforward process in most cases. We will be mainly using the Hue/Saturation Adjustment and the Color Blending Mode.
We’ll start with the Hue/Saturation adjustment. Find the channel that matches the hair color the closest, which in this case will be either Cyan or Green. Don’t worry if you’re not getting to the precise channel, as Photoshop will auto-correct that for you.
Using the Eyedropper tool from the adjustment panel (not the regular Eyedropper tool), Shift+Click (or click on the Eyedropper Plus icon next to the regular one) and drag it along her hair to add colors to the Hue channel. You should notice the Hue slider at the bottom of the box changes slightly as it collects the data from your image.
Once you think you’ve gotten a pretty decent color range, slide the Saturation slider to the left to maybe around negative 90-95%. We don’t want -100% as that completely takes out all the color and makes it look fake.
You can also play around with the Hue and Lightness to make the hair look more natural. I.e. if the scene is a tad warm, we should probably move the Hue slider to a Orange-Red hue. And depending on the amount of light in the scene, the Lightness should be bumped up or down a notch. Check the screenshot below to see my personal settings.
Pretty good. You can see that a bit of her ear’s color got taken out, so this is where the Color Blending Mode comes in.
Make a new layer and name it to something like Fix-up and set the layer’s Blending Mode to Color. This will allow any color fill or brush stroke over it to only affect the hue of the layers below. It’s probably better if you try it out yourself with some random colored brush to see its effects.
While still on the Fix-up layer, select the regular Eyedropper (I) and sample some part of her skin that has a similar hue. I would recommend her ankle as the saturation there is milder.
Hit B for the Brush. Set the Brush opacity to maybe 15–20 and slowly color in the ear and any other areas you feel the colors transition seems too unnatural.
Repeat the Eyedropper/Brush process with other colors to patch up the edges around her hair and the brick wall, her hair and her face, etc.
Done!
This should be where you’d normally stop, but for this picture, the fringes around the top of her head really bothered me. Since this picture was low-res enough, I made an additional layer and literally just painted over it with a rougher brush at a low opacity to make the transition more natural there.
I also used the clone tool in combination to clean up her hair a bit more. So at this point, it really comes down to your preference and your eye for these sorts of things. It takes practice to get better, but you’ll get there.
I hope it helps!