Here's how to get R installed quickly.

On a Windows machine

1. Either: Visit the R project. Click the "CRAN" link. Pick a CRAN site near you. Click the "Windows" link. Click the "base" link. Download (e.g. right click and choose "Save Link As...") the link that is called something similar to R-2.7.0-win32.exe.
2. Or: click here to download the latest Windows version of R from the UK CRAN mirror.
3. Run the resulting executable and accept all its defaults.
4. Fire up R with (e.g.) Start > Programs > R > R 2.7.0. You'll see something like this:

Under Ubuntu Linux

See http://cran.r-project.org/bin/linux/ubuntu/README.html.

sudo apt-get install r-recommended

then run it with:

R

Under Ubuntu Linux, with the current version from CRAN

Add this line (edited appropriately) to /etc/apt/sources.list:

deb http://my.favorite.cran.mirror/bin/linux/ubuntu version/

For example:

deb http://cran.ma.imperial.ac.uk/bin/linux/ubuntu lucid/

Then

gpg --keyserver keyserver.ubuntu.com --recv-key E084DAB9
gpg -a --export E084DAB9 | sudo apt-key add -
sudo apt-get update
sudo apt-get install r-base r-base-dev