Note that sometimes when you plug in a monitor you have to press a button on the keyboard to switch from laptop screen to monitor. You can then press the button again to switch to both.
Pressing the button continuously wraps around from laptop screen only, then monitor only, then both screens, then back to laptop screen etc.
It is often a combination of the Fn key and a key along the top (one of the "F" keys). You may see a small icon next to the key showing a small "monitor" icon.