Method 1 is to convert the image to greyscale (image>mode>greyscale in photoshop). This converts the three RGB values for each pixel into one 8 bit value striping all the colour information but only allows the storage of the grey value of each pixel. This creates a smaller file size. This method is useful if you are are going to send the image as an attachment or are uploading it to the web.
Method 2 is to desaturate ( image>adjustments>desaturate) the image. This converts the three RGB values for for each pixel into B/W by making each of the the values the same ( eg red 150 green 150 blue 150).
Both of the above methods deny you the ability to modify your conversions based on the original hue and are realistically a one size fits all solution.
Method 3 is to use photoshops inbuilt black and white conversion dialog box (image >adjustments >Black and white). This is only available in later versions of photoshop. By moving the sliders you can adjust how your conversion is done depending on the original source hue information This allows you to adjust the contrast between nearby objects in the image that are similar in lightness but disimilar in hue, which you can’t do using the first 2 methods.
Method 4 is to use channel mixer (image>adjustments>channel mixer) . This can be used if you only have an earlier version and you dont’ have the black and white conversion dialog box use channel mixer to convert an image to black and white you must tick the monochrome box on the bottom left of the dialog box and the move the sliders. When you move the sliders make sure that they add up to near 100 but not to much above 100 because you can risk clipping the highlights , that is the bright parts of the image.
Of the 4 mentioned methods the one I prefer is method 3 because of the degree of control over the conversion that it gives me. If I have to use software without it I use channel mixer.