What I have done with mine is to cut them low on the stem, I wash them and then make sure they are totally dry. Then if you have a dry dark place in your house you can ties the stems in bundles and hang them upside down to dry ( this is mainly if you want to use them for decorative purposes). With the cooking herbs I strip off the leaves after they are washed and dried then put the leaves in a cardboard box with a lid and keep it in a dry place until they are totally crisp then put them in a container. With my basil, after washing I take 2 packed cups and process it in a food processor with about 1/8 c. of olive oil then freeze it in ziplock bags. When I want to make pesto all I do is defrost it, add 1 c. parmesan cheese, 2 -3 cloves garlic, 1/8 c. ground and toasted pine nuts, and about 1/2 -3/4 c. more olive oil.
I just realizd I got carrried away and this is more info than you asked for, but I'll leave it as is.
