My Google Drive is full. Rather than delete old email, I want to save it to a local hard drive. Once I have selected the messages, how do I move them (download them) to my computer?
It depends on what you want to do with the messages once you have them stored "locally".
If you just want to file them away, possibly to restore them at some future date, I'd say use Google Takeout. Google Takeout export the messages in
mbox format, which many email clients can manage.
If you want to be able to work with them, I'd say use a local email client (e.g., Thunderbird) and connect to your account via IMAP. Then you can move messages between local and "Gmail" folders, effectively deleting them from Gmail but keeping them available in your mail client to search, respond to, etc.