Download Outlook for from the App Store and then open it. The icon looks like one of these:

If it's your first time using the Outlook for app, enter your full email address, then tap Add Account.

If not, open the Menu > tap Settings > Add Account >Add Email Account.

If you're asked to select your email provider, please choose Office365

Enter your email account password and tap Sign In

Accept any prompts for permission you may receive.

Swipe through the features and you're now ready to use Outlook for iOS!