How can I connect my 2015 Macbook Air to both ethernet internet and to external monitor ?

This should be simple, but because Apple has altered the ports on Macs over the years, it might be tough to figure out which connectors you actually need to connect a monitor to your Mac.
Follow the instructions below to figure out the Apple adapter and cable you'll need to connect your Mac to your monitor.
Connect it.
Select Displays from the System Preferences menu.
Navigate to the Arrangement tab.
Remove the checkbox for Mirror Displays (unless you want the second screen to show the same content as your original screen).
Drag the illustrated displays into the desired configuration.
One of the panels will have a white menu bar at the top. Drag this white bar on the screen you want to be the centre of attention.
Go to System Preferences > Monitors > Arrangement and select Mirror Displays to mirror the display on both (or many) displays.
If you choose 'Show mirroring options in the menu bar when available,' a status menu will appear in the menu bar, making it easy to toggle this off and on.

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