We don't use much oregano in our cooking, so there's no way for us to use it all fresh. These are the steps I used to dry it.
Trim full sprigs off of the plant. I cut right above any signs of new leaf growth as to encourage those baby new leaves to become big fatty mature leaves. Then it's on to the actual drying.
1. Group the sprigs into bundles of 10-20 and tie with a loop of ribbon or string.
2. Poke holes in the bottom of a paper bag and put the bundles inside the bag (one hole per bundle).
3. Pull the ribbon or string through the holes.
4. Hang in a cool, dry place. (I used our basement).
5. Let dry for 2-3 weeks.
You can store the fully dried sprigs in a ziplock bag in the freezer, or an airtight container in a dark cabinet (like store bought herbs). When it comes time to use them, pull the leaves off the stem and crumble them!