To access an Outlook account on your iPhone, use either the native Mail app or Microsoft's own version of Outlook for iOS devices. How you go about setting up your Microsoft Outlook account varies slightly depending on which of these two solutions you choose.
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Use the Native iOS Mail App
Open the Settings app on your iPhone and select Mail, Contacts, Calendars.
Choose Add Account on the main Mail, Contacts, Calendars screen.
Select Outlook.com as the account type on the Add Account screen.
Enter your name, full Outlook email address and your Outlook account password in the provided fields. Tap the Next button in the top-right corner when you are finished to complete the account setup.
Use the Microsoft Outlook App
Open the App Store on your iPhone and search for the Microsoft Outlook app. Open the app's details page in the App Store, tap the Free button and follow the prompts to download and install the app on your iPhone.
Open the Microsoft Outlook app after the installation completes and select Add Account.
Choose Outlook.com as your account type.
Enter your full Outlook email address and associated password in the provided fields and then tap the Sign In button.
Tap Yes to confirm that you want the Outlook app to synchronize your messages and other data.
Outlook Web App
If you use the Office 365 platform, there is an iOS version of the OWA for iPhone app you can install on your iPhone to access your account. The app is a free download from the App Store, but you must be subscribed to the latest version of Office 365 for Business in order to use it.