Bill Bryson's
Shakespeare: The World as Stage (Atlas Books, 2007), an installment in the "Eminent Lives" series, is a succinct biography of the Bard, offering "just the facts," (of which, as you either already know or will learn quickly from Bryson, there aren't very many at all) along with a survey of the various biographical speculations that have sprung up over the years.
While not quite as laugh-out-loud funny as some other Bryson books, this does have its amusing moments, and is quite readable. I liked that he avoided the speculative flights of fancy that have afflicted other recent Shakespeare biographies; as a good introduction to the playwright, it's seems to me quite a good choice.