I've a free Yahoo! Mail account nearing 300 emails and I want to download the mail to my computer. I also have a backup of the emails in a Gmail account.
Is there something in Yahoo! Mail that will help me download all my email?
Yahoo supports POP with a paid account (and as of December 2013, with standard accounts as well). Gmail supports POP and IMAP - set up a mail client like Thunderbird according to the instructions provided by the mail provider and that's about it.
Thunderbird should save by default. To be sure, go to Tools -> Account Settings -> Synchronization & storage, and ensure Keep messages for this account on the computer is ticked for that account