You need java to run Onyx, which you can download at https://java.com/de/download/ if you don’t have it installed (many system have by default). Once java is installed, you can just download the onyx.jar file and start it with java (on windows systems, doubleclick on a .jar should automatically start it with java). There is no installation necessary.
Do you have a windows machine? And have you tried downloading the onyx.jar and then double-clicking it? If you didn’t find the downloaded file, your browser may over a list of downloaded files where you can choose to run it from. Or did you start the file and it gave an error message?