How can I see the game progress of my friends?

You can see your Facebook friends' game progress in two different ways.

Tap on the “Leaderboard” button located between the Areas and Home buttons on the game's bottom navigation bar. After that, tap on the "Friends" tab on the upper navigation bar to see the progress of your friends.
You can see your friends' game progress by going to the "Leaderboard” tab located between the Areas and Home buttons on the game's bottom navigation bar. While on that tab, tap on the "Friends" tab on the upper navigation bar to see the progress of your friends.