Open the "Play Store" app

Using the search bar at the top search for "Outlook". Then click the top result titled "Microsoft Outlook" with a blue outlook icon. Click the button titled "Install". The app may ask for permissions but click "Ok" in the bottom right and the app with download and install 

Once the application has downloaded you will be able to find it either on your home screen or by clicking "Open" on the app's page in the app store. You will then be prompted to add your account. Enter your email address and click "Add Account". You will then be asked to enter your password.