Caledon has given an excellent and brief summary of what transpires in William Shakespeare's Macbeth up until the point where Lady Macbeth goes mad. I would add just a few things to complete the picture and point out one of the great ironies of the play.

It is true that Macbeth has had some felicitous tidings from three hags known as witches; they predict that Macbeth will be Thane of Cawdor, and soon he is, though no effort of his own. It is a simple reward by King Duncan for his loyal valor on the battlefield. The witches predict he will be king, and soon he is; however, this only happens because Macbeth and his wife successfully plot against and kill Duncan while he is a guest in their own home.

After Duncan's sons flee, fearing they will blamed for the deed, Macbeth is crowned king, and thus begins a reign of bloody terror in Scotland. He cannot let his friend Banquo live, as Banquo knows about the predictions and will no doubt call Macbeth to account for the king's death; so Macbeth makes sure Banquo dies. Macbeth reigns in a state of paranoia, and he has spies everywhere. He kills Macduff's family just because Macduff does not attend the banquet to which the king invited him. for example. 

Things get even worse as Macbeth revisits the witches and gets three more "predictions" which assure him (because he wants to believe) that he is practically invincible. Unfortunately for him, Duncan's oldest son Malcolm has teamed up with Macduff and a British army and they are advancing on Macbeth's castle. This is when Lady Macbeth has begun to go a little crazy out of guilt for what she has done. 

Now for the irony. When Macbeth was experiencing a horrifying guilt for having murdered the king, Lady Macbeth was quick to dismiss his feelings and tells Macbeth to quit worrying about the blood on his hands:

You do unbend your noble strength, to think
So brainsickly of things. Go get some water,
And wash this filthy witness from your hand.

Obviously Macbeth is concerned more about the figurative meaning of the blood on his hands (the fact that he has murdered a king) than the actual blood, but Lady Macbeth blithely tells him that a little water is all he needs to be fine. When she goes a little mad, she tries in vain to wipe imaginary blood from her hands, an ironic twist on what she once told her husband. Apparently a little water is not enough to rid oneself of such guilt.

Macbeth is a Scottish nobleman who encounters three witches who prophesize that Macbeth will become king. Macbeth is seduced by the thought of himself as king, and is encouraged by his wife to invite the current king, Duncan, to their home, under the pretense of a banquet. Macbeth murders Duncan as he sleeps, and inherits the crown. However, his guilt over the murder, as well as his jealousy and growing paranoia, quickly make him into a despot, and cause him to murder many others, including his friends and their children. Macbeth's wife begins to go mad because she feels she is at least partially responsible for this, and despite her ambition and encouragements, she doesn't really have the stomach for a life filled with guilt.