Detailed instructions for running and developing shiny applications with R can be found here: http://shiny.rstudio.com/. But it's easy to run the basic app.
1) Make sure that you have two files, ui.R and server.R in your working directory and a data directory containing the various .Rdata files.
2) Install R and all of the required packages listed on the "prerequisites" https://sourceforge.net/p/shinycgh/wiki/Prerequisites/ wiki page.
3) Start R and type:
library(“shiny”)
runApp()