In addition to the standard single connection commonly used, so that the switching is controlled exclusively by the software, it is often possible to make use of two separate connections. Depending on the particular machine and the BIOS, you may be able to connect to two different ports–for instance, one VGA and the other HDMI.
Multiple monitors are managed in MX Linux with Start menu > Settings > Display. You can use it to adjust resolution, select whether one clones the other, which ones will be turned on, etc. It is often necessary to log out and back in to see the display you select.
Finer control of some features is sometimes available with xrandr. Xfce 4.12 has some limitations with multiple monitors, but 4.14 has expanded capabilities including storing two different configurations.