Download the Windows zip file for your OS type (usually the 64 bit version) from releases.
Unzip this file and run openttd.exe.
Download and use one of the Linux builds in releases, or compile from source (see below).
Download and use the MacOS DMG file from releases.
Alternatively, use homebrew by typing brew install jgrennison-openttd --cask.
See compiling for more details.