The Chess.com Notifier Add-on for Firefox checks regularly whether it is your turn in one of your current chess.com games. It then notifies you by displaying a little icon in your Firefox status bar. A double-click on this icon directly brings you to your next ready game.
Please download the newest version from HERE (Mozilla Addons) and follow Firefox's instructions to install (click Install). Please note that the add-on is still in beta-status, meaning that it might contain bugs and might not always work as intended.