I produce a fair amount of agricultural charcoal (biochar) to improve the soil in my garden. It's incredibly simple to make. You burn wood through the "gas" phase and then deny oxygen so it can't burn in the "carbon" phase.

In practical terms: make a fire in a safe pit, keep adding wood, and continually tamp down the pieces that have stopped burning vigorously and have turned to carbon. Than, dampen it slightly, cover to exclude all oxygen, and let it sit until cold.

You can also heat wood that's stuffed inside a closed (not sealed) vessel. You'll get less ash this way. An uncoated tin can with a foil cover is an easy way to experiment.

Activation of the charcoal is a separate process, and I'm not sure a backyard setup could do this effectively. Though since my charcoal finishes while exposed to some steam and some CO in a sealed environment, I wouldn't be surprised if it is activated to some degree (can't prove it though).