Growing basil out of cuttings is a pretty easy way to propagate basil plants. You can even root basil cuttings from refigerated already-cut basil stems from the grocery store!
All you need is a small cutting that's at least 2 inches in height, with a few small leaves at the top. Try cutting the stem at a 45-degree angle. For example, you can cut a piece of basil that looks like this:
Then place the cutting in water and wait for 1 to 2 weeks for new roots to grow. Make sure that the stem of the cutting is not too long, or the cutting may not grow roots. If your basil cutting isn't growing roots, don't worry since you can grow basil in water too! If you think the stem is too long, you can cut it shorter and wait again to see if roots will grow.
When the basil cutting starts growing roots, you'll see tiny roots growing out the bottom of the cutting and along the stem like this:
The roots will continue growing in water. You can continue growing the basil cutting in water for as long as you'd like. Just be sure to change the water once in a while.
Afterwards, you can transfer the rooted cutting to a small pot with potting soil to continue growing it. Expect the cutting to grow more quickly if it has larger roots before you transfer it.
I will post updates from the picture of the replanted basil cutting above. Stay tuned!