What do I need to buy to use an external monitor on my Mac 12 inch retina display?

You may get your answer here --> Use multiple displays with your Mac - Apple Support

Connect the displays

• For each display, securely connect a video cable (and adapter, if necessary) from a video output port on your Mac to the video input port on the display. See About the video ports on Mac.
• If your Mac has one or more Thunderbolt ports , you can connect up to two displays to those ports. If the displays also have Thunderbolt ports, you can connect one display to another, and then connect one of the displays to a Thunderbolt port on your Mac. Or you can connect each display to different Thunderbolt ports on your Mac.

Set up some displays for mirroring and others for an extended desktop

If more than two displays are connected to your Mac, you can specify that some displays use mirroring, showing the entire desktop, and other displays show the extended desktop (displaying the desktop across two or more displays). For example, if you have three displays, you can have two displays showing the same information and the third display showing the extended desktop.

1. Use the task above to set up all the displays as an extended desktop.
2. Press and hold the Option key and drag one display icon onto another display icon to mirror those two displays.