I agree with the recommendations of Strunk and White. One of its virtues is that it's very short, and not very dry (except for the humor). And you can probably even find a cheap used copy, because it's been reprinted over and over. A few points here and there are a bit dated or a bit quirky, but on the whole it's still surprisingly useful.
For particular usage questions, two modern choices, both more suited for reference or browsing than reading from cover to cover:
Burchfield, ed., Fowler's Modern English Usage, 3rd ed. (Oxford, 1996)
Garner, Dictionary of Modern American Usage (Oxford, 1998)
I agree with Amy-MiMi that reference works like the Chicago Manual or the MLA Manual are more about the nitty-gritty details such as punctuation and format.
'Eats, Shoots, and Leaves' is a popular recent book on punctuation, but according to several reviews I've seen, it's not entirely reliable.
I agree with Joe W that much American TV and many American movies (though not all) are pretty bad, and that the BBC is usually pretty good -- as is its US counterpart National Public Radio (NPR). But I'm not sure you can learn much about style just by listening, partly because it all goes by so quickly, and partly because radio (and TV) programs tend to be written to tighter deadlines and therefore of necessity less carefully edited.
I still think the best suggestion is just to read. Read a lot, in different styles, by different writers. Don't just get the two-sentence highlights from CNN or USA Today <double flinch>; read a longer article in a better-quality publication, e.g.:
newspapers: Guardian, Times, Independent, Telegraph (all UK), NY Times, Wall Street Journal, Washington Post, LA Times (all US), Toronto Globe and Mail (Canada)
magazines: Economist (UK), Atlantic Monthly, New Yorker, Time, Newsweek (all US)
Of course, books are the best reading of all, but without knowing what you like and dislike, it's hard to recommend particular writers. There should be many past discussions in the archive, as the topic is a perennial favorite. If you don't find enough suggestions, drop by the Literaturfaden (Mr Darcy et al.) or open a new thread in the chat room.