Ask for a personal Homepage if you do not have one
In ~/public_html create one folder for each shiny app and copy your R scripts there. Grant access to your files (only necessary if you created new files) by executing setwww in a linux console.
URL to your app: http://shiny.math.uzh.ch/user/<NAME>/<FOLDER>/ where
NAME is typically your lastname, lowercase
FOLDER is the subfolder in public_html with the scripts