If you want to connect to a network on nm-tray left click the icon in the system tray. If you have a wired connection with DHCP it should connect automatically. If you want to disconnect your from a network under active connections left click to disconnect. To connect to wifi left click on the nm-tray applet and connect the wifi name applet and then enter the password for the wifi.
After connecting to a wifi your known connections will by left clicking on nm-tray of wifi connections under known connections. The list of active connections are networks you are currently connected to. The list of wifi networks is listed under wifi networks you are connected to.
To get information on your current connection to the network your can right click on nm-tray connection information to get info on your current Ip address connection speed and driver in use for the connection. To toggle notifications on connecting and disconnecting to networks right click on the nm-tray tray icon and check or uncheck the checkbox for enable notifications.