Firstly, make sure save all Office 365 apps if there is any open. After you closing all opened documents, confirm they have synced on OneDrive properly. 

Open any of blank document in Word or a blank spreadsheet in Excel. 

Before you create or open any document, find the Account button on left menu.

You will see your logged in details and also there is an update options button. Click on it and choose Update Now.

If there is any update, it will tell you to download and install. Before the installation, it will ask you to close all applications.

If all apps are up to date. You can close the screen.