Installation is very easy. Just follow the below steps.
Just navigate to https://apps.shopify.com/mps-notify-me page and click on the Add app button as 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 Notify 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 button. Just press the Install button as shown on the below snapshot and you will reach to Notify Me app installation final step.
In the last step, you just need to choose your Notify Me app plan. Notify Me has Paid as you grow plans. So just choose a plan that fits best on your store based on the number of products you are selling and Notify Me will start monitoring all products(and variants) of your store.