Make sure that you have the Xtensa toolchain and ESP-IDF installed (instructions).
The build was tested with esp-idf at commit be81d2c16d7f4caeea9ceb29fece01510664caf3, but it should work with master (if not, open an issue so we can look at it).
After setting up the toolchain, compile the firmware with
make defconfig
make -j4
Then, turn on your badge while holding the * key. The screen backlight should start flashing, this indicates that you can load the firmware on the ESP32 with
make flash
After flashing, turn the badge off and on again to start using the new firmware.
Make sure that you have libsdl1.2-dev and cmake installed, then from the root of the project
mkdir emulator-build
cd emulator-build
cmake ..
make -j4
./Linux/ihc-badge-linux