Here’s a Photoshop tutorial that “uses two adjustment layers to lower the vibrancy of the photo while preserving some colors.”
Well, fine, but why go to that trouble? All you need to do to achieve this effect is to duplicate the image, change it to grayscale with whatever technique you prefer, and then apply the image in whatever percentage gives the best result.
Here’s the before and after from the tutorial.
Here’s the result using my simpler technique. I just changed the mode on the duplicate to grayscale but of course there are other ways to desaturate, which might be better. I could have matched the above image exactly but I couldn’t stand how murky and low contrast the original image was, so I couldn’t resist fixing it using my usual Photoshop adjustments technique.
Why complicate matters?