R can be downloaded and installed from the Comprehensive R Archive Network (CRAN). The download mirrors can be found here: http://cran.cnr.berkeley.edu/.
The downloaded R files contain standard installation wizards. If needed, operating system specific installation instructions can be found here: http://cran.fhcrc.org/
As noted in the What is R Page, there are many integrated development environments (IDE) for R. These IDEs provide an enhanced user interface and in general yield a more streamlined user experience. RStudio is a popular IDE and will be used extensively on this site. Downloading and using RStudio is highly recommended as an alternative to the standard R package interface. Note that RStudio requires that R already be installed on the system. RStudio can be downloaded here: http://www.rstudio.com/ide/download/desktop
The downloaded RStudio files contain standard installation wizards.