While there are plans to offer Resonite from various sources (such as alternate storefronts or as a first-party download), it is currently distributed through the Steam storefront.
Windows
Download and install via Steam.
Linux
Resonite is currently in a playable state on Linux, but is strictly not feature complete to the windows version.
Install Resonite from the Steam store page.
Issues
When launching Resonite, the logo will appear as a test card; however, Resonite should start as expected. This is currently a known bug.
Additionally, some features, such as the desktop mirror and clipboard functionality, may not work as expected.
For additional help in getting VR working see: Linux VR Setup