The tutorials on this page describe various approaches to monochrome conversions. Some are possible in almost any basic image editor, others rely on the capabilities of advanced editors such as Photoshop.
There is no "best way" of monochrome conversion that will suit all images. However, there are some approaches that will consistently give better results that others. Exploring the various conversion techniques will not only make you better at monochrome conversion, it will also give you a better understanding of whatever image editor you use.
The most important thing to learn from this tutorial is that producing good monochrome images requires an understanding of how to control colour and contrast.
This tutorial explains a monochrome conversion technique that gives a lot of control over the process and is particularly useful if you want to produce a high-contrast result.