Download your platform's AudioMoth Flash App and follow the in-app instructions.
AudioMoth can be programmed with different firmware over USB through this application. AudioMoth firmware files all use the .bin extension and can be downloaded through the Flash App, directly from the Open Acoustic Devices Github page, or built yourself.
If your current firmware does not support automatic switching to flash mode (default firmware older than version 1.3.0), you will need a metal paperclip to manually put your AudioMoth in a state where it can be flashed. Instructions for switching are found in the app itself. Click File and then Show Manual Switch Instructions.