Run make zephyr, this will clone the Zephyr Project repo or update it if you've already done it before
Now you can build the project, follow one of this options:

Trying on a simulated board

The default board is an x86 machine that can be simulated with QEMU, and runs inside a Docker container, you only need to have Docker installed. Its Ethernet is also simulated and uses the TUN/TAP interface. You'll need a TUN/TAP interface (default name is tap0) on your host machine; follow the instructions here to configure your network to provide a suitable networking environment.

Run make build. The interface configuration on the simulated machine side is in the file overlay-e1000.conf, and defaults to tap0. You can change this overlay file adding an OVERLAY argument (e.g.: make build OVERLAY="-DOVERLAY_CONFIG=something").
Once the build succeeds, run make run to run the target. The default Docker configuration is to share /dev/net/tun; if this does not work for you, pass the necessary Docker parameters inside SHARETUN (e.g.: make run SHARETUN=something).

Using a real board

Run make build BOARD=yourboardname (e.g.: make build BOARD=nucleo_f746zg)
Once the build succeeds, run make flash. The Makefile shares the USB bus with the Docker container, this works well with ST-Link and J-Link devices. If this does not work for you, pass the necessary Docker parameters inside SHAREUSB (e.g.: make flash SHAREUSB=something)
The generated ELF file is at build/zephyr

Cleaning up

You can run make clean to clean up the build files but keep the configuration files, which speeds the next build
If you do major changes (like compiling for a different board...), run make pristine to clean up everything under the build directory.