There are many ways of converting a picture to black & white and I don't believe one is better than the other. You just have to find what works and produces the best results for you.
Here are some of these techniques that I applied to a picture of myself for better demonstration.
1. IN CAMERA
Most cameras today —DSLRs and point & shoots — allow you to shoot directly in black & white by changing a setting in the menu. Although probably the easiest method, I wouldn't recommend this as all the camera does is desaturate the original color image.
Done in Photoshop (or some other post-processing software), this is basically the same as above. All it those is remove all color information from the image. This leaves you with a rather flat, gray picture still needing quite a bit of work.
4. CHANNEL MIXER
Another great method is to use the LAB channels to convert your image to black & white. What we are doing is selecting the LAB colorspace and isolate the A & B channels to retain the Lightness channel only. Start by switching your colorspace from RGB to LAB. Then, go to your channels pannel and select the Lightness channel. Now go back and convert your colorspace to grayscale. This will isolate channels A & B. Come back to your layers pannel and your picture is converted to black & white.
Last and not least, is my favorite option for converting my pictures to black and white. I use a plugin by Nik Software called Silver Efex. It allows you to control a lot of aspects and especially specific zones in your picture to produce stunning black and whites.
As a conclusion I would say it is important to find a solution that suits your needs.
Here are the 5 different outputs again so you can see them side by side.
I hope you enjoyed this and feel free to add a method or ask a question in the comments.