Episode 3 in the Proxmark Basics series gets in-depth with the Proxmark 3 RDV4.01 - the cornerstone of RFID research.
The Proxmark 3 has evolved significantly over the years, leaving a trail of incomplete and outdated information, specifically in regards to updating firmware.
Updating firmware depends on the hardware you're running, the modules it uses, and the operating system that you use.
If you're using Windows, check out the Proxmark 3 Windows Firmware update tutorial:
If you're using Linux, check out the Proxmark 3 Linux Firmware update tutorial: