From the home screen, tap Settings
Tap Mail, Contacts, Calendars
Tap Add Account
Tap Microsoft Exchange
Enter your email address in the field labeled 'Email'
Leave the 'Domain' field blank, and enter your email address in the field labeled 'Username'
Enter your password, making sure to double-check spelling, capitalization, punctuation, and numbers. Leave Description as-is, and tap Next. If you get any server errors or warnings, tap Continue.
In a few moments, a new field titled 'Server' will appear. It should be pre-populated with the correct server address. If it is not filled in, enter "m.outlook.com" (w/o quotes). Tap Next.
Confirm that all items are turned ON, and tap Save. You're finished setting up your account. Next, we'll make sure you're using Office365 as your default account for mail, contacts, and calendars.
When you return to the Mail, Contacts, Calendars settings page, scroll down until you see the Mail sub-heading. Look for the 'Default Account' setting and tap it. If you don't see it, skip to step 12.
Tap the name of the account you just set up. It should be called 'Exchange' or the name of your organization. This step sets your Office365 account as your default email account.
Tap the back arrow to return to the main settings page. Scroll down until you see the Contacts sub-heading. Look for the 'Default Account' setting and tap it. If you don't see it, skip to step 14.
Tap the name of your Office365 account, which you just set up. This will make Office365 your default contact list. When you create a new contact, it will go into this list from now on.
Tap the back arrow to return the main settings page. Scroll down to the Calendars sub-heading. Tap the Default Calendar line. If you don't see it, you're all finished!
Tap 'Calendar' to make Office365 your default calendar. All new calendar entries will go to Office365 automatically from now on.
That's it! You can now start using your iPhone with Office365. Remember, it may take several minutes for your mail, contacts, and calendars to start downloading and get synced, so please be patient.