Download the appimage file in the Download section to a location of your preference. Before using this download all the data files from https://geant4.web.cern.ch/support/download. 
The data files can be huge and time consuming to download but they are required for G4Studio to run properly. After downloading them, extract them in a folder (for example g4-data).
Double click on the appimage file and you will see the UI coming up. You will need to set the paths to the datafile appropriately without which the program will crash. 
For further questions, please write to deepaksamuel@gmail.com