You can download R from here: http://cran.cnr.berkeley.edu/
Note that you download the same file if you are updating or installing for the first time. You'll have to know your operating system (Windows, MacOSX, or Linux) and which version of that operating system you are using in order to download the correct file.
If you have a Mac, the regular R program provides a nice interface, but it has been recommended to me by PC users that RStudio offers a better user experience for Windows. RStudio is also available for MacOSX if you prefer. You can find RStudio here: http://www.rstudio.com/