If your mailbox comes close to the storage capacity limit, you will receive a notification. Then you have the option to upgrade to a larger storage package in your Premium account.
The storage capacity is shared between all user accounts. So if you have multiple users, you do not need to order for each user account. Here you can see the storage upgrade options.
Please remember that Tutanota values your data highly: All data is encrypted and we never send any advertisements to your email account. Please support our fight for privacy and upgrade to Premium!