Great Question! The shortest route for anyone who wants to gain access to their Office 365 documents is actually directly within Word, PowerPoint, Excel, etc.; not signing in online! Here's how, from Microsoft:
Sign in to an Office desktop application
If you have the current version of Office, open any Office application and, in the top right corner, click Sign in.
If it is your first time signing in to the Office Application it may invite you to "Sign in to get the most out of Office: on the Recent page:
If you see the name for your account, you're already signed in.
Type the email address and password you use with Office.
Which account should I use while I'm using an Office application, I have a personal one too!?
Since you may have two kinds of Microsoft accounts, like a personal Microsoft account accounts you created and accounts from your work or school that use Office 365, be sure you are signed into your MCA account!
To switch between accounts in an Office application, click your name in the top right corner and click Switch account.
Sign out of an Office desktop application
In the Office application, select File > Account.
Under User Information select, Sign out.