I try to overwinter as many herbs as possible, indoors, and use them judiciously until they put on new growth. Oregano dries great in a paper bag (wash, then air dry for a day before bagging), along with some other middleweight herbs like tarragon and chives. Tougher stuff like rosemary and thyme — I just keep them going. Basil, parsley and other tender herbs get used up in an orgy of herbaceousness in the fall, then I save a few plants to keep going in the kitchen until next year’s seedlings are underway. (I plant extra so I can harvest micro basil, arugula, etc. around March-April.)
For seed saving in the fall, I let the seed pods mature on the plant, then snip them off (no leaves) just before they totally dry out. Hang them up in a closed paper lunch bag (writing what it is on each bag) to finish drying for a few weeks, depending on humidity, in the shade. Shaking loosens most of the seeds and is a good indicator of when they’re thoroughly dry, then you can pick out the stems and fan the chaff away gently.