First, download Outlook from the iOS App Store. Here's the icon:
If you have never used Outlook for iOS, before, enter your full email address, then tap Add Account.
If you have used Outlook previously, go to Menu > Settings > Add Account > Add Email Account.
On the next screen, enter your email password and tap Sign In.
If you have multi-factor authentication on your account, verify your identity through the steps on the next screen.
Then you should be all set!