The latest release is v0.4.0. All modern Linux distributions should be supported, but please file an issue if you have problems.
Once you have completed the download, extract the zip archive to your preferred location, such as your Desktop.
Depending on your distribution, you may be able to double click sulis inside the folder to launch the game. Alternatively, open a terminal, change to the extracted folder's directory, and type ./sulis.
You can configure the display mode, user interface scaling, animation speed and keybindings in the Options menu. This configuration is saved to ~/.config/sulis/config.yml
This file also contains some additional configuration options not present in the UI.
There is a guide available for getting started playing the game.