i leave on stem also.. takes up less space this way. also if you just cut the main stem just below the stem your triming, it makes a little hook. So its really easy to hang on a line.. i cut every branch off the plant like this and trim one branch at a time.. then hang.
Unless the room is very humid then, like everyone said, i wouldnt worry about it 2 much. just opening the door to the room that they are hanging in once or 2ce a day is prolly good enough air flow for them to dry. if they aint dry after like 5-7 days.... then you prolly need more air flow. REMEMBER... the slower they dry the better/smoother they will taist.