Unlike many other services, FastMail has full support for logging in to multiple accounts at the same time. When you go to our homepage, you will be shown any currently logged in accounts. Select one to go to the account's Inbox. To log in to another account, click the "Log in to another account" link at the bottom of this list.
If you tick the Keep me logged in option when you log in, then going to our home page will take you straight to the Inbox. To log in to another account in this situation, go to https://login.fastmail.com.