How can I use the Steam app to download a game I already own?

App Instructions

On the left menu, click on your name to bring up your profile. Scroll down to your list of games and click "View All Games".

From here, it will list all games you own, whether or not they are installed, and include an icon that will allow you to install them remotely.

Website Instructions

Go to your games list (accessible by going to your profile, then clicking Games), which will be at a URL like steamcommunity.com/id/[YourID]/games/.

From here, click on the "All Games" tab. This will show you which games you currently have installed, and will include an icon that will allow you to remotely install any games that are not installed.