Free coins can be earned by clicking the shop in the top right corner. You can choose to complete offers such as watching ads, installing games, survery, ec. Once it is complete the coins should arrive within 1-2 minutes.

This option sometimes does not show up for people. Sometimes the video does play, although the survey doesn't work as till yet. Hopefully they can fix this.

Coins not showing up? Visit The Road to Survival Game Guide for tips

As of the October 6, 2015 update, free coins have become severely restricted, as to what was allowed in previous versions of the game. If you are lucky you might be able to watch 10 videos per day, for 3 coins each. Other offers such as surveys, and game downloads, are bait and switch, where they initially claim on the list screen to offer more coins, but when you click on the one you want to do a new screen opens up with dramatically less coins. Also many do not work as they should and you will not receive your coins even if you follow the directions.

In other words, the game has been severely imbalanced towards the Pay to Play model.