To install R visit the website https://cran.rstudio.com/, where you'll find download links to all major platforms.
Download and install following the instructions and keeping all default settings.
R is a command line program. On Linux it looks like this:
Luckily, there are some Graphical User Interfaces (GUI) to R. If you're on Windows, R is already shipped with one. If you click on the R icon you'll see something like this:
This is a very basic GUI and we recommend to use the RStudio interface (*).
RStudio can be downloaded and installed from www.rstudio.com.
Again, simply follow the instructions. If you open RStudio it will look like this:
*Note, that there are many more user interfaces available, e.g. Tinn-R (Windows only) or the RCommander. See here for an overview.