I have dried rosemary, and it was fairly easy. I just put the sprigs in a small plastic basket. You can line the bottom with paper towel. Leave on the counter. When you think it is dry (1 2 weeks?) strip the leaves from the stem and put in your jar. You could also cut a few sprigs and just hang to dry.
I don't worry with it now., Rosemary, if it gets established out does itself here. I have one huge one in the front garden. It is evergreen, so use fresh year 'round. When parts of it extend their boundaries lop off with pruning shears. I have another I put in another flower bed. I saw what was happening, and moved it to a designated spot in the back yard.
Hope this helps