If you're new to the R language but keen to get started with linear modeling or logistic regression in the language, take a look at this "Introduction to R" PDF, by Princeton's Germán Rodríguez. (There's also a browsable HTML version.)
In a crisp 35 pages it begins by taking you through the basics of R: simple objects, importing data, and graphics. Then, it works through several examples of linear models (formula basics, fitting a model, model diagnostics, analysis of variance and even regression spones). Finally, there's a section on Generalized Linear Models, with a focus on logistic regression. The document doesn't attempt to explain all of the capabilities of R, but instead works through a series of examples to teach by demonstration. All of the datasets used in the guide are available online, so it's easy to follow along from home.
Also by the same author: a guide to R for Stata users.
Germán Rodríguez: Introducing R