Click the circular avatar icon on the top right to expose the account menu and then click "Account Settings".
Locate the email addresses tab and type into the text field to add an email address. Click "Add" when you're done.
Before you can use this new email address, you must verify it. To do this, open your email account, look for this email, and then click "Confirm Email".
If you refresh your account settings page, you should now see that your new email address has been added. You might want to add secondary email addresses as a backup in case you lose access to your default one.
If you would like to make your new email address your new default, simply click the drop down menu next to the email you wish to make default and then click "Make default".
If successful, the email addresses card in your account settings should now look something like this: