Thyme can readily be propagated by cuttings, but I'm not a fan of rooting them in water when you can root them directly into a small container with some good potting medium.

THANK YOU
I WILL DO THAT.

If your pot is large enough, you can propagate thyme by layering. Select a branch/stem that's close to the surface of the soil, and cover it with soil (potting mix). Keep it down with a piece of wire bent over. It will form roots, and you can then separate the baby from the mother.

Striking cuttings in water is not a method recommended by horticulturists. Best to strike them in their natural medium (dirt!). For thyme, cut off as long a stem as you can, snip off the new growth, and use the next section down.

Once you stip off the new growth, do you then just plant the whole stem in the dirt? Or do you leave part of it above the dirt?

I've uprooted a mature thyme bush and divided the rootstock in two, using a sharp knife. I then planted both back, with good results.

Hairpins (not bobby pins) make perfect holders for securing the stem down onto the soil surface while rooting. This works for a lot of plants and in many cases you don't even need to brush any dirt on top of the stems. I like greystoke's method, too, since it provides "instant gratification"!

That is a great tip about using hairpins! I'm going to use it for my pansies. Thanks!!