You should start by going to the official R website: http://www.r-project.org/. From this website, you can download the R program and also find links to many manuals for R available as PDF files. These manuals vary in their complexity. Below I list some introductory ones that I find helpful. I also list additional resources in case you want to explore the R project further.
"An introduction to R. Notes on R: A Programming Environment for Data Analysis and Graphics", by W. N. Venables, D. M. Smith, and the R Development Core Team. This manual introduces the R environment, and gives the most important commands you have to know to get started. It also has an introductory session in the appendix that teaches how to create and manipulate different objects, do basic graphs, and perform simple statistical analysis. Doing this session is an excellent way to become familiar with the program.
"Using R for Introductory Statistics ", by John Verzani. This document explains the basics of R, including commands for data manipulation, exploratory data analysis, confidence interval estimation, hypothesis testing, and linear regression. It is intended for an introductory statistics course. It is targeted entirely to beginners. It also has a useful list of resources at the end.
"R for Beginners", by Emmanuel Paradis. This document explains the basic commands for data manipulation, graphing, statistical analysis and programming with R. It also gives a short introduction to the R environment, and explains the different types of objects that are manipulated by R. It is targeted entirely to beginners.
"The R Guide", W. J. Owen. This manual gives a short overview and history of R, and explains the basic commands to manipulate data, perform vector and matrix operations, graph, and perform statistical analysis with R. One of its advantages is that it is very concise. Of course, this comes at the price of less examples, but it is a very economic way of covering many topics.
"Using R for Data Analysis and Graphics. Introduction, Code and Commentary", by J. H. Maindonald. This manual covers more advanced topics, but it also contains almost-introductory sections about the R environment, vector and matrix manipulation, data structure and plotting. Its main advantage is that it contains introductory exercises, and provides answers for some of them.
"R Data Import/Export", by the R Development Core Team. This document explains how to export and import data to/from R.
"Econometrics in R", by G. V. Farnsworth. This manual explains how to use R to perform basic econometric analysis. Although it presupposes some knowledge of econometrics, it is accessible and clear. It also covers very basic math operations, plotting commands, and programming commands. This should not be the first manual you read. But it could be helpful when we start doing basic econometric analysis.
The R website contains many other documents. Check the R Manuals section and the Contributed Documentation section to find them. You can also take a look at the Comprehensive R Archive Network (CRAN), a network of ftp and web servers around the world that store identical, up-to-date, versions of code and documentation for R. You may also want to consider the Frequently Asked Questions of this website, since they can give you a good idea of what R is and how it works.
If you are interested in having an easy-to-use editor, you can download the Tinn-R editor from here. If you want to make a long-run investment in an editor that you will be able to use for much more than R, you may want to consider Xemacs. Professor Jasjeet Sekhon provides several resources on how to install XEmacs and ESS (Emacs Speaks Statistics) on a variety of operating systems.