Downloading messages

How does one get copies of messages so they can the be removed and free up storage? I have seen a response to this question that says you cannot do this, however the iPhone itself indicates otherwise. I don’t know how to download messages but would like to. I went round and round from one apple page to another and to my iCloud account to no avail. So while it suggests me to download the messages so I can delete them and free up space, I can find no path to do so.