|Please note that these instructions refer to using OWA on Exchange server 2010, not the more recent Exchange server 2013. For the latest OWA instructions, please see Using Outlook Web App.
If you are not sure which version of OWA you are using, please refer to this document.
You can check the amount of storage left in your mailbox by pointing the cursor on your name at the top of the Mail folder list. The window that appears shows the current size of your mailbox and your mailbox limits as shown below.
Each Exchange email account is setup with 15 Gigs of storage.