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 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!