Pick a "Semi-Hardwood" stem, one that isn't entirely green or entirely brown (hardwood cuttings can be taken from some plants in the winter, but not what I'm doing here). It should be able to bend slightly, but also be able to snap easily if creased.

Take the cutting, find a leaf node near the brown/green transition zone, and then cut the stem at an angle right below the leaf node.

Remove the leaves from the next 2 or 3 leaf nodes up (so no leaves are under the soil when you plant it), and then cut any leaves above it in half. This is so the plant will still benefit from the leaves' photosynthesis, but doesn't require the full amount of water and nutrients that large leaves would require.

(Optional) you can then dip the bottom of the cutting in Rooting Hormone, Bontone II is what was recommended in the workshop I took. If you don't have any, plants should still be able to root just fine without this step.

Then you can stick the cuttings in your soil medium. I use a mix of coco coir, perlite, and vermiculite- the same mix I use for seed starting. Sterility is the main concern, as you don't want your cuttings to become diseased. You can sterilize your soil by pouring boiling water over it.

I see people use perlite, vermiculite, sand, or a mix of any of these things- just don't use unsterilized compost or unsterilized potting soil. These cuttings need to remain moist for months, so if left in regular dirt they will most likely rot.