Meson releases can be downloaded from the GitHub release page.
Meson is also available in the Python Package Index and can be installed with pip3 install meson.
The newest development code can be obtained directly from Git
Meson is implemented in Python 3. If your operating system provides a package manager, you should install it with that. For platforms that don't have a package manager, you need to download it from Python's home page.
Depending on your platform and backend you wish to use, you might need the Ninja executable. Again, use your distro-provided version if possible. Otherwise download it from Ninja project's web site.