Set up the pico-sdk as described in the Getting Started guide and set the PICO_SDK_PATH environment variable. Then run zig build. A firmware.uf2 should appear in the zig-out.
The current configuration is for the Pico W and this is basically the Pico W blink example. You can set -DPICO_BOARD at the top of build.zig.
Like in the C Version, you need to adjust the linked libraries in the CMakeLists.txt.
To build this example with the regular non-W Pico, remove the pico_cyw43_arch_none library from CMakeLists and rewrite main.zig to not use the W-specific cyw43 functions.