The following are free online resources for learning how to use and troubleshoot R. Many more resources can be found online, including an R-specific search engine can be found at rseek.org and R section of the question-and-answer site Stack Overflow.
Introducing R, by Germán Rodríguez
A readable and gentle introduction to basic concepts for R.
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 Core Team
A manual for using R written and maintained by the core R development team. Provides extensive detail, possibly too much for someone first wading into the software.
Population Health Data Science with R: Transforming data into actionable knowledge, by Tomás J. Aragón
A comprehensive open-source e-book that provides the basic for epidemiological analysis using R.
Impatient R, by Patrick Burns
General reference tool for basic ideas and concepts in R.
R Inferno, by Patrick Burns
Help identifying problems that will haunt you in R. Useful for looking up why something has gone wrong or unexpectedly in R.