Converting a coloured image into black and white can often be achieved with just a single click when using even a simple photo editor. However, the resulting image may not always be pleasing. Often this is the result of not having a good enough tonal range and the image looks "flat". To achieve the classic high contrast look in a black and white image, one of the easiest ways is to use the dodge and burn tool in Photoshop.
Here's how. First, use whichever method you prefer to change a coloured image into black and white. For instance, click on Image>Mode>Grayscale, or, Image>Adjustments>Black & White.
Now, using the Burn tool and setting the Range to Shadows and Exposure very low (to, say, 3%), brush over the entire image to make the dark areas slightly darker. Then using the Dodge tool and setting the Range to Highlights and Exposure again to very low (say 5%), proceed to brush over the image again to make the bright areas slightly brighter. That's all there is to it!
Below is an example of an image before and after the Burn and Dodge treatment.
Before Burn and Dodge