Answer: Oregano is relatively easy to dry successfully. However basil is difficult to dry well because it does mold and discolor unless dried quickly. Also, the flavor tends to deteriorate when dried. For these reasons many people like to make it into pesto and freeze it, or put it in an ice cube tray with water or broth and make ice cubes that can then be stored in plastic bags and used by dropping them into soup or stew later, or you can make flavored vinegar with it. (It is not safe to try to preserve herbs in olive oil at room temperature.)
The National Center for Home Food Preservation offers the following guide on drying herbs. I would add to their instructions that you should pick the basic when it is dry (no dew on it) and on as dry (less humid) a day as possible. Make small bundles to allow better air circulation between the stems. An indoor, air conditioned area tends to be less humid and have good air circulation so that can be helpful as well.
You may need to cut and paste the complete url to make it work correctly.
How to dry herbs
They also explain how to freeze pesto
or make herb flavored vinegar
I hope this gives you some ideas.
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