Open Outlook for iOS. The icon looks like this:
If you don't have it yet, download it from the Apple Store.
NOTE: Available for iOS devices using iOS 9.0 or higher.
Go to Settings > Add Account > Add Email Account.
NOTE: First time using Outlook for iOS? Just tap Get Started.
Type your full email address, then tap Add Account.
NOTE: If you're asked to select your email provider, you may have to set up your email as an IMAP account.
Enter your email account password and tap Sign In.
NOTE: Have 2-step verification? Get detailed steps on how to set up an Office 365 email account with 2-step verification.
Tap Yes or Allow to give Outlook permission to sync calendar, contacts, etc.
You're now ready to use Outlook for iOS!