You cannot launch apps in the App Store unless they have already been downloaded to your device.
To download an App, tap on the "GET" button (free apps) or the price (paid apps) to initiate the download / purchase.
click here ➜ Download apps and games on your iPhone or iPad - Apple Support

Once it's downloaded, the app should appear on one of your home screens or in the App Library. You can then just tap on its icon and it should open.
click here ➜ Open apps on iPhone - Apple Support
In the App Store, downloaded apps will have an "Open" button instead of "Get" or a price. You can tap the Open button to open the app.