R package
You can download the R package from the The Comprehensive R Archive Network (or CRAN). CRAN is a network of web servers around the world that store identical, up-to-date, versions of code and documentation for R.
If you have questions about downloading or installing the software, or what the license terms are, please consult the answers to frequently asked questions.
R vs. R Studio
RStudio is the most popular Integrated Development Environment (IDE) for R. It includes a console, syntax-highlighting editor that supports direct code execution, as well as tools for plotting, history, debugging and workspace management.
RStudio is available in free or commercial (paid) editions and runs on the desktop (Windows, Mac, and Linux) or in a browser connected to RStudio Server or RStudio Workbench (Debian/Ubuntu, Red Hat/CentOS, and SUSE Linux). The free version of RStudio can be downloaded here.
Note: You need to download and install both R and RStudio separately in order to use RStudio.