You can earn Coins by:

1. Achieving the Bonus Goal when you play a level.
2. Inscribing Lost Words in the Library.
3. Earning Stars to open Star Chests.
4. Collecting Hoot-Loot from the daily spinner (and watching a rewarded video ad to get a second spin). 
5. Collecting the free 25 coins per hour from the gift icon on the Home screen (or watching rewarded video ads to get increasingly higher numbers of Coins.)
6. Finally, if all those sources of Coins aren't enough, you can buy packs of Coins in the Shop!