Most people use either lump or charcoal briquettes, so we’ll focus on the process for each as it is very different.
Lump Charcoal: Is typically made from leftover from sawmills, furniture manufacturers and others. It is then put into a large container, heated up to combustion temperatures, but since oxygen is restricted, it does not ignite. However, all the water and some volatile compound is extracted. This process can take a day or more. An interesting note: if you ever bought a bottle of ‘liquid smoke’, this is basically leftover from this process. Water vapor infused with wood smoke.
Charcoal Briquette: The same mill who processed lump charcoal is left with small pieces and charcoal dust that cannot be re-sold as is. They mix this dust with binders such as starch then compress it into briquettes and baked to harden them up. Other manufacturers use sawdust from mixed wood from lumber mills. Once this sawdust is turned into charcoal it is mixed with various additives. This is then molded into their pillow shape.
Since briquette manufacturers do not provide a list of ‘ingredients’ of the binders used, some people are concerned about additives. Some brands have responded by offering ‘Natural Hardwood Briquette” which contains no binders.
If you want to see an interesting video about the whole process, click on this YouTube video.