How do you leave a game in Dota 2?

You can find menu/search_for_game screen button at the top left. When you go there you will see leave button at the place where you have search panel usually - at the middle of the screen.

Click the top left arrow icon to open the main menu, then click the Disconnect button in the middle of the screen or at the bottom right of the screen (in Dota 2 Reborn).

If you also want to abandon the game and search for a new one, press Leave Game (under Reconnect) after you disconnected.