Play techniques in bridge should be divided to two:
Techniques in the play of the hand
Terence Reese, a prolific author of bridge books, points out that there are only four ways of taking a trick, and two of these are very easy
* playing a high card that no one else can beat * trumping an opponent's high card * establishing long cards (the last cards in a suit will take tricks if the opponents don't have the suit and are unable to trump) * playing for the opponents' high cards to be in a particular position (if their ace is in front of your king, your king may take a trick)
All trick-taking techniques in bridge can be reduced to one of these four methods.
The optimum play of the cards can require much thought and experience, and is too complicated to describe in a short article. However, some basic ideas of probability may be considered:
Some of the most important probabilities have to do with the position of high cards.
* The probability that a given opponent holds one particular card, e.g. the king: 50% * The probability that a given opponent holds two particular cards, e.g. the king and the queen: approximately 25% * The probability that a given opponent holds at least one of two particular cards, e.g. the king or the queen: approximately 75%
When developing long cards, it is important to know the likelihood that the opponents' cards in the suit are evenly divided between them. Generally speaking, if they hold an even number of cards, they are unlikely to be exactly divided; if the opponents have an odd number in the suit, the cards will probably be divided as evenly as possible. For example, if declarer and dummy have eight trumps between them, the opponents' trumps are probably (68% chance) divided 3-2 (one opponent with three trumps, the other with two) and trumps can be drawn in three rounds. If declarer is trying to play with a seven card trump suit, it is more likely that the outstanding trumps are divided 4-2 (48%) than that the cards are evenly divided 3-3 between the opponents (36%). 
Basic techniques by declarer
When new to the game, a player should be familiar with these strategies for playing the hand:
* trumping * crossruff * establishing long suits * finesse * General suit management * holdup (mostly at NT contracts) * managing entries * when to draw trumps
Advanced techniques by declarer
Someone who plays regularly in tournaments should be familiar with these concepts:
* counting the hand (tracking the distibution of suits and high cards in the opponents' hands using inferences from the bidding and play) * coups and elimination * duck * dummy reversal * endplay * safety play * squeezes
Basic techniques by defenders
* opening lead * when to lead trump * suit management * discarding
Advanced techniques by defenders
* avoiding an endplay or squeeze * counting the hand (tracking the distibution of suits and high cards in the unseen hands using inferences from the bidding and play) * opening lead - using information from auction * signaling * uppercut
the best explanation for various bridge playing techniques, is to first explain a playing technique, as used by the declareer, and then explaining a defender technique used to thwart that particular declarer technique.
The most basic technique is using long suits.
Suppose you are playing 3NT and uyou are holding the following two hands:
S: AKQxxx H: xxx D: xxx C: A
S: Jx H: KQJ D: KQJ C: xxxxx
West starts by cashing his heart and diamond aces. He now plays another heart, and you have to plan the play. You can immediately see two heart tricks, and two diamond tricks, no matter what you chose to discard on west's two aces (you probably discarded the two jacks, which is not always optimal, but that's deception, so we shall deal with it later, for this hand, it makes no difference.)
So, counting four tricks is good. you can also see another four in dummy, so that's almost the nine you need. Where are you going to get more tricks from?
Let's see. there are only thirteen spades, and you are holding eight of them. that means that you opponent are hoding only five. Chances are they are divided 3-2 between the two of them. but you can make you contract even if they are divided 4-1, providing that you play carefully enough. you should cash all your hearts and diamonds from the declarer hnd, than cash the spade jack, which would hold the trick. You then play a small spade to the AKQxx left in dummy. You play the high cards first, and unless you are very unfortunate, the low spades will take tricks too. the opponents will have no spades left by that stage. Oh, don't forget to take the club ace too. You will end up with two overtricks.