My work mailbox says it is full at 50GB and I can not send or receive. How can I increase it?

The limit comes from the license. Exchange Online Plan 1 gives 50GB and Plan 2 gives 100GB. Your admin can change the license, which is the direct way to a bigger mailbox.

Other options:

1. Online Archive. Admins can turn on an archive mailbox (not on all plans) and a retention policy moves old mail there. It appears as a second mailbox in Outlook.
2. Clean up. Empty Deleted Items and Recoverable Items, delete big attachments and old calendar items.
3. Export old mail to a PST in Outlook and move it out of the mailbox. Keep the PST backed up.

Ask your admin which of these your plan supports.

Admin turned on the archive. Mailbox below the limit again. Thanks.