Congrats on your successful herb garden @Artemisia- it looks like you’ve got a beautiful harvest ahead! 
I second the vote for hanging the herbs to dry, I know a lot of people have good luck with that method- just be sure to hang them in a place with low humidity/moisture, or they can get moldy!
For a quick way to dry them, you can spread washed herbs out on a baking sheet and pop them in the oven on a low temperature (leaving the oven door open slightly to minimalize moisture). There’s a video here that walks through this method:
For storage, you’ve got lots of options! 
My personal favorite is keeping glass jars with pretty labels (maybe even some fun Witchy Herb Labels)
Alternatively, you can also freeze fresh herbs- they stay for a long time in the freezer and make a great additions to soups and dishes. It’s a nice touch of freshness you can have at hand all winter long 
Blessed be and enjoy your herbal harvest! 