Some people lightly scrape one side of the cutting, near the base, these injured parts tend to root better in some cases.

Dip the bottom part of the cutting into rooting hormone, either in powdered or liquid form, and tap the excess off. Insert the cutting 1/3 to 1/2 way into your pot of growing medium at a slight angle. Half perlite and half-potting soil is good, or half-potting soil and half sand.

Some people enclose the pot in a plastic bag and tie at the top to support a high humidity level. The pot should not be in direct sunlight. I have a place out of the wind on the north side of the house, where it gets some light, but no direct sun.

After a month, check for root growth by lightly pulling on the cutting. If it resists, that should mean there are roots. Gently lift out the new plant and re-pot. Let it gradually get used to its new environment by setting it out for a short time, then lengthening that time each day.

I've also had good luck layering thyme. Using a well developed plant, just mound soil around the base up to several inches deep, covering as many stems as you want to root. Within a few weeks, each branch will have begun to root where covered, and can be divided and potted up individually. The mother plant can regenerate more, or be left to recover from the trimming.

Look at the stems on your rosemary carefully. Towards the lower ends of the branches, you might see some small knobbly growths coming out. These are adventitious roots- dormant, but ready to grow. Pieces of rosemary with these root VERY easily, sometimes just sticking them in garden soil during a rainy spell is sufficient. You may be able to do layering on a rosemary, if the plant has a base-branching form, like described for the thyme.

good luck,
PS, the herb forum has experts far more experienced than me!