In Photoshop there are several ways you can turn a coloured image black & white and this tutorial will demonstrate a few of them. All produce various results and some are more complicated then others so just take a look, have a go and see which you like best.
First, we'll start off by simply desaturating the image.
Open your image and go to image>adjust>desaturate and once you've clicked, your image will be black & white. Simple.
The image before and after desaturate was applied.
Next, you can use the channels window to turn your image to black & white. You'll notice you have RGB, red, green and blue channels and by clicking on the red, green and blue channels individually, you'll see your image change. All three channels create the black & white appearance with a slightly different tone.
Once you find one you like, go to select>select all then Eedit>copy and past the new image into a new layer or document.
See how using the different channels change the image.
Finally, we'll be using an adjustment layer.
Open your image and create a new adjustment layer ( hue/saturation)
either in the layers panel or by going to layer>new adjustment layer>hue/saturation.
This will open a new window where you can rename the layer, once you've done this click ok. From here, another window will open with three sliders in: hue, saturation and lightness. Pull the saturation slider down to the left and you'll see it changes the colour of the image. You can also more the lightness slider to make the image darker if you wish.
Once you're happy click ok and your image is complete.
How changing the saturation can make an image appear to be black & white.