Login to your Office 365 portal and navigate to:
where you should see the above screen.
Select the Word Online icon.
Word Online will now launch and you should see the splash screen you see above prompting for Dropbox integration.
Select Add Dropbox account and enter yoru Dropbox account details if prompted.
Once you have entered your details you will see in the top a drop down menu with options for OneDrive for Business and Dropbox as shown above.
In the bottom left as well, you will see the above locations you can select to open a file from, OneDrive for Business and Dropbox.
If you select Open from Dropbox you will be able to navigate your Dropbox file locations and select a file.
The first time you select a Dropbox file you’ll be prompted to allow Microsoft Office Online to access Dropbox as shown above.
Select Allow to proceed.
You’ll now be able to edit that document in Word Online.
In the bottom of the window in the middle you will see that any updates you make are Saved to Dropbox automatically.
If you now go into your Dropbox at any time and select an Office document you can elect to open it with the appropriate Office Online application.
Pretty handy if you are using Dropbox in some capacity along with Office 365. I couldn’t see a way to open from say Dropbox and save to OneDrive for Business for example, hopefully we’ll that edition in the not to distant future.