Best Connected functionality is built into BT Access Manager which automatically selects the best available network from the installed network profiles, based on what is available to you.
To connect, click on the centre button. Not sure how to do this? see opening BT Access Manager
Depending on which network profile is active, you may be asked for configuration details, for example, the wi-fi network to connect to, before the connection can be established. When connected, the centre button changes to show a solid green circle and a tick.
To disconnect, click on the centre button again.