I have used sermon handouts almost as long as I have been preaching. It is probably that teaching side of me that seems to cause me such difficulties. Anyway, it is something that I have used for a couple of decades and not given much thought to. In fact, I am probably in a rut as to how I use them. I just simply shoot the major points with fill-in blanks to one of my secretaries and she copies & pastes and it’s done. For better or for worse.
But Craig Webb has a helpful article on sermon handouts. He gives some good uses/purposes of handouts:
It encourages people to participate and engage the sermon by writing something down. This is an added level of learning to your speaking and the visual images they see on your PowerPoint.
It eases the tension of persons who were unfamiliar with the Bible and are afraid of the clumsiness of finding a particular Bible reference.
It allows me to share different translations and paraphrases of familiar passages.
It provides a take home reminder of the content of the sermon. Members and attenders can share these with family or co-workers. At one church I served, we provided notebooks for members to keep sermon notes.
He also gives four simply but good suggestions for improving sermon handouts. He also attaches a .pdf with some samples of different styles of handouts.
You can find his complete article here.