If you grow organically, there's no need to wash them but if you do, make sure the leaves are very dry (either spun dry in a salad spinner, or thoroughly pressed between towels to remove all the moisture).
Remove any ratty leaves and spread the herbs out, stems and all, in a single layer across a baking sheet. Try not to overlap them too much as you want air to circulate between the leaves.
Set your oven to its lowest temperature setting; mine hovers around 200°F. Once it's preheated, place your tray of herbs on the center rack and prop the door open slightly with a wooden utensil to allow some air movement.
Then (important step!) turn the oven off and let the herbs dry inside while the heat slowly dissipates. This method ensures the delicate leaves won't burn.
Once the oregano is cool enough to touch, pull the leaves off the stems.