First, you can only Pin apps on your iPhone, iPad, or iPod touch. You must also have the (free) Pinterest app installed on your iOS device.
Once installed, you can search the App Store for the app you want to Pin. When you find it, tap on it to bring up the “details” view, as shown in the image below.
Use the “Share” button to pin the app.
Then tap the “Action Button” (the box and arrow) at the top of the details to bring up your options for sharing the app. If you don't see Pinterest in the list of options, tap 'More' and slide the switch to enable it. Once it is enabled you'll be able to Pin the app.
Yes the app icon will look weird while pinning. And no comments in the pin.
From the share panel you can tap on Pinterest and choose which board to share on. From there it appears on your board like any other pinned item, as shown in the image below.
Behold my pinned app! And be completely surprised I have a board full of geekery.
If you see an app on someone else's board that you want to install, you can tap on the pin and it will take you to the App Store and directly to the app that was pinned. I've tried it and it works pretty well, even with no way to add extra commentary. Hopefully Apple and Pinterest are on to something that will sincerely help with app discovery.