On some older Chromebooks, Developer Mode could be turned on with a physical switch that could be flipped. However, on newer devices you will need to boot the device into Recovery Mode.

To start, make sure your Chromebook is on. Then press the Esc and Refresh keys and then press the power button.

Normally the refresh key is where the F3 key would be, and is normally the fourth key from the left on the top most row on a keyboard.

Your device should take you to a screen that says something along the lines of "Chrome OS is missing or damaged", signifying that you have arrived at the recovery screen.