“Impatient R” provides a brief grounding in the basics of using R.
Beginner’s Guide to R from Computerworld.
Try R is a fun way of learning some R.
swirl (Statistics With Interactive R Learning) is another interactive environment for learning R.
There is a set of two-minute videos called R twotorials.
One Page R (which in total is many pages) covers a number of topics.
There are many books about R. The best one for you to start with depends on where you are and where you want to go. If you are starting from zero, then I recommend R For Dummies.
R is a good way to avoid problems with spreadsheets.
See also “Why use the R language?”
R and finance
R is used a lot in finance, and that use is growing. There are two task views that are pertinent:
The R language category of the Portfolio Probe blog has examples of R being used in the context of quantitative finance.
Other R resources
There are several other R task views.
The R-bloggers site aggregates blog posts about R.
There are R user groups around the world.