Two books come to mind as useful introductions: Paul Fussell's Samuel Johnson and the Life of Writing (New York: Harcourt, 1971; London: Chatto and Windus, 1972), and Thomas Woodman, A Preface to Samuel Johnson (London: Longman, 1993). Woodman is probably more useful for rank beginners and newcomers to the eighteenth century; people who've read some of Johnson's works will get more out of Fussell, who has more interesting critical takes.
Some other possibilities: Donald J. Greene, Samuel Johnson, 2nd ed. (Boston: Twain, 1989); Walter Jackson Bate, The Achievement of Samuel Johnson (Oxford: Oxford Univ. Press, 1955); and Greg Clingham, ed., The Cambridge Companion to Samuel Johnson (Cambridge: Cambridge Univ. Press, 1997). Robert DeMaria, Jr., recently published The Life of Samuel Johnson: A Critical Biography (Blackwell: Oxford, 1995), which is better as a critical introduction than as a biography.
A handy book to have around is Pat Rogers, The Samuel Johnson Encyclopedia (Westport, Conn.: Greenwood Press, 1996). But it's often superficial, sometimes inaccurate, and always too bloody expensive for most mere mortals to own.
This is part of a Guide to Samuel Johnson by Jack Lynch. Comments are welcome.