There are two situations that we have to consider.
1) you DO know your old email password.
2) you forgot your old email password.
Once logged in, drop down the menu in the right upper corner and click on Password and Security.
Have your tech administrator login to the hosting control panel and set the password for you.
Once logged into the hosting control panel, click on E-Mail Accounts.
From there, click Manage next to the email address you are working on: