Installation is very easy. Just follow the below steps.
Just navigate to the https://apps.shopify.com/mps-promote-me page and click on the Add app button shown in the below snapshot.
Once you click on the Add app button if you are not already logged in then Shopify will ask for your store URL (myshopify.com version), just insert your store URL where you want to install the Promote Me app and click on the Login button, as shown in below snapshot.
Once you will click on the Login button, you will see the next screen with the Install app button. Just press the Install app button as shown in the below snapshot and enjoy the awesome features of the app.