Answers are checked automatically. Whenever you have three things right the game should automatically let you know and then tell you what you had right.
There is a bug with some adblockers I have run into where they occasionally freeze up the game and have it stop automatically checking for answers. There are no ads in the game, so I don't know what causes this, and its very, very rare (only two or three people out of everyone who has played the game has run into this)