The faster the herbs dry, the more flavourful the resulting dried herb will be

Conventional Oven:
Place clean dry herb sprigs on a foil-lined baking sheet. Bake at the lowest setting until herbs are dry and brittle. This should take about 12 hours.
Strip leaves from stems and place in small airtight storage containers.

Air Drying:
Tie small bunches of herbs with string and hang upside down by the stems in a dry warm spot out of direct sunlight.
Be sure air circulates freely around the bunches. Let dry till leaves are brittle. This usually takes a few days to a week, depending on the thickness of the leaves.
Pick off the dried leaves and store in tightly covered containers in a cool, dry place.

Microwave Drying:
Pick herbs when the dew has just gone off. Put on paper towels on a plate in the microwave. Zap on high for a minute to start . At that point they appear "wet".
Stir them, zap again for another minute, move around again, and zap approximately 30 seconds more or until they are dry and crumbly.
Rub between your hands to break up, pick out any twiggy parts and put in small jars.
Mark the date on the container of your dried herbs. They can be kept for one year. Heat, moisture and light rob herbs of flavour

Freezing Herbs:
Wrap in foil or plastic wrap. You can also chop clean herbs, place in ice cube trays and fill with water.
When needed remove herb ice cubes and drop into hot cooking liquid.
You can also wrap bunches of fresh herbs in foil or plastic wrap and freeze them for several weeks. You should expect some discoloration of frozen herbs..

Some herbs also may be frozen. Rinse herbs in cold water and blanch in boiling, unsalted water for 50 seconds. Cool quickly in ice water, package and freeze.
Dill, parsley, chives and basil can be frozen without blanching.

You can also make herb butters and herb vinaigrette.