All that you need to do to get started is to put your twitch username in the username field on the options page. A link to the option page can be found under "Tools" > "Extensions" > "Twitch notifications".
Clicking a notification will open the stream in a new tab.
The source is on github: https://github.com/mickelus/twitchNotifications. Feel free to submit bug reports, feature requests or pull requests.