Rosemary cuttings (take 10cm cuttings of soft new tips) grows very easily simply stuck in a jar of water and left on the window sill. People say these sorts of 'water roots' aren't as strong as the sort you get from planting in the ground, but if you want a year round guaranteed method, it's the easiest. Once they've formed 2cm long white roots dangling from the base, you simply pop them into a pot or directly in place in the garden. Rosemary is most vigorous in the warmer months so don't be disappointed if you plant these in winter and find they are slow to take off. They soon will as the temperatures rise.
Another easy method is to look for parts of the main plant which have been resting on the ground. Often the plant will start to root at this point (and you can deliberately force this to happen by pinning a piece of the large plant down onto the ground and covering it a little, then wait a month or so).
And you can see, that gently lifting the part that had contact with the ground reveals some roots.
I cut this section free of the main plant...
and then trimmed the top and side to make a neater shape above the roots.
Next, I potted it up and gave it a quick water. There! All done!
So simple, and within a few weeks new growth will be apparent.
I will prune the new growth and keep in the pot for a a bit longer until I know the roots have really taken hold.
Then it will either go into the ground or be given away. So simple!