You will still receive notifications regarding chats/calls/messages the regular way in your LiveAgent panel whether or not you choose to receive Desktop Notifications.
Once you have your first incoming chat/call your browser should ask you to allow Desktop Notifications and you can simply allow them to start receiving them for all future sessions.
If you don't get this pop-up window you have most probably declined it earlier. In this case, it is possible to enable Desktop Notifications manually, simply follow the directions for your browser.
For Google Chrome:
The example in Google Chrome: