Now, whenever Gmail is open in Chrome, you’ll see notifications of new e-mails, as per your settings. When you’re done make sure that you scroll to the bottom of the page and hit the ‘ Save Changes‘ button to save your settings - don’t just close the tab! With desktop notifications enabled you can go pick one of the three notification options listed:
Gmail has a built in option for it, all you have to do it turn it on!
The best part about this tip is that you do not need to install any sort of fancy-pants desktop app, panel applet or browser add-on to get notified of new mail.