Oregano and maybe some of the mint are the only two I think dry well at home.
Depending on the volume you're doing, the microwave works suprisingly well. http://www.organicgardening.com/learn-and-grow/dry-herbs-microwaves.
Depending on your humidity, you can air dry. Tie them in small bundles on the branch but not too tight so the air can flow and hang them up to dry. Some other ideas for you to consider are http://nchfp.uga.edu/how/dry/herbs.html