A 64-bit operating system is required and a minimum of about 4GB of RAM are needed to process most songs, more for songs longer than 3 minutes. Virtual machines and 32-bit systems are not supported.
The Windows installer will guide you through the installation process. If you encounter problems with the installer, you can also install from a .zip file. If you have Dell Backup and Recovery installed, there is a known bug in that software that causes AnthemScore and other Qt-based programs to crash when you try to open a file using the file dialog. You can fix this by upgrading or uninstalling Dell Backup and Recovery or simply drag and drop audio files onto the side panel rather than clicking the 'Open' icon.
To install on OS X, download and click on the .dmg file and drag the app to the Applications folder. Then right click and choose "Open". Double clicking will not work, since the app comes from outside the Apple store.
To run on Linux you also need to install Qt and create link_to_qt in the AnthemScore directory. See the README for details.