STEP 1:             

Open Outlook for iOS. The icon looks like this:


iOS Outlook app 


If you don't have it yet, download it from the Apple Store.


STEP 2:             

Go to Settings > Add Account > Add Email Account.


Note: First time using Outlook for iOS? Just tap Get Started.


Outlook app settings 

Tap Add Account 


STEP 3:             
Type your full email address, then tap Add Account.


STEP 4:             

Enter your email account password and tap Sign In.


Enter your Outlook.com password 


STEP 5:             
Tap Yes or Allow to give Outlook permission to sync calendar, contacts, etc.


Allow permissions. 


STEP 6:             
You're now ready to use Outlook for iOS!


Source.