West opens with a weak three-bid. What does it mean if you, North, make a takeout double?
This is one area where bidding can be difficult. You would like to have the perfect hand for a takeout double: 4-4-4-1 distribution and 14-plus high-card points. However, that does not often happen. Instead, you must do the best you can. A three-level double is for takeout, but you could also have a big balanced hand with no stopper in the opener's suit, which would keep you from overcalling three no-trump.
How does the advancer (doubler's partner) react? He tries to do something intelligent! But he always remembers that he is assumed to hold six or seven high-card points. Advancer should jump the bidding only with at least three points more than that (or a very distributional hand). Otherwise, he makes a minimum bid in a suit, or advances with three no-trump (with goodies in opener's suit and a preference for offense), or passes (with goodies in opener's suit and a preference for defense).
In this deal, after South bids three spades, North, assuming six or seven points opposite, raises to game.
West cashes his two top diamonds, then shifts to the club jack. South wins with dummy's ace and draws trumps. What next?
Declarer must find the heart queen. But West is already known to have started with two spades, seven diamonds and at least one club. And by playing a club, South can learn more about West's hand. What becomes clear is that East is a heavy favorite to have the heart queen, so declarer takes the finesse that way.