Rules & Etiquette
Long hesitations during the bidding and play will be distracting for your opponents, your partner, and you! Always try to bid and play at a steady pace.
You may also be giving away information about your hand - if you stop to think for too long during the bidding, your opponents may guess that you hold a strong hand - if you pause before playing a low card, your opponents will often deduce that you hold an honour in that suit, and will adjust their play accordingly. You must not deliberately pause in order to mislead your opponents.
What if my partner hesitates?
You must ignore the hesitation. If your opponents feel you have used unauthorised information gained from the pause, they are entitled to call the director. If the director is satisfied that your bid/play is not justified by the cards you hold and the bid/play to that point, he can amend the contract/score and penalise you.
That does not mean to say that you mustn't bid on - if you can justify the bid you make by the cards you hold and your partner's and opponents' bids, that's fine. In other situations, your partner's hesitation may lead you to think he has a weaker hand than the bidding implies - when that happens, you have to carry on as though his hand is as strong as he has bid, and if you pass with a hand where most people would bid on, your opponents are entitled to call the director as well! If your bid or pass is borderline, you are likely to get called up for it.