First, separate the leaves from the stems, rinse them if necessary, and air dry. In Beautiful Easy Herbs (Rodale, 1997), author Laurence Sombke then recommends the following: "Place a single layer of leaves on a paper towel on a microwave-safe plate. Lay another paper towel on top, and microwave on high for one minute. Watch the herbs continually during the drying process, and stop the oven if you smell the herbs burning. If needed, repeat the heating for 30 seconds at a time until the herbs are fully dry."
On its website (geappliances.com), GE Appliances warns against using paper products containing recycled material in a microwave, since these may include bits of metal that can arc or ignite.
Because of their relatively low moisture content, herbs are about the only thing that can be dried successfully in a microwave oven. Other foods, such as tomatoes or berries, contain too much moisture and wind up cooked rather than dried.