How does Lady Macbeth change Macbeth's mind after he decided not to kill King Duncan?

When Macbeth tells his wife 'We will proceed no further in this business,' she criticizes firstly, the fact that he has now suddenly reneged on a promise which she metaphorically compares to a hope expressed by a drunk. She furthermore appeals to his honor and brings into question his bravery. She intimates that Macbeth is a coward, having moved from 'I would' to 'I dare not' - allowing his previous expression of intent to be influenced by his fear. She compares him to a cat that wishes to eat fish, but is afraid to get wet.

Macbeth obviously feels insulted and states that he has the courage to do everything required to prove his manhood, there is no man who would do more. Lady Macbeth's response is to ask him what kind of a savage had then made him break his promise to her. She makes it personal. She tells her husband that when he dared to murder Duncan, he was more of a man and he should now strive to be better than that man he had been before. She tells him when he was all determined to proceed, nor time nor place had been a consideration. She says that the time and place is now ideal for him to commit his deed, but that these are exactly the factors which prevent him from acting.

To indicate her determination and to encourage her husband, lady Macbeth employs a horrific metaphor by saying that she had breastfed and knows the tenderness that one feels for the baby which one is feeding, but that she would pluck such a baby from her nipple and dash out its brains if that is what she had promised to do, in much the same way as Macbeth had promised. Her husband, though, is still not convinced and considers the possibility of failure.

Lady Macbeth expresses shock that her husband should even consider failure. She asks that he regain his courage and then lays out a plan as to how they would assassinate the king. She mentions that she would provide Duncan's guards with so much wine and spiced ale that they will soon become drowsy and then fall fast asleep. Duncan will, because of his long journey, be in a deep sleep. With the guards and their charge being so indisposed, it would be easy to kill Duncan. The blame for Duncan's death would then fall squarely on the shoulders of his drunk guards.

Macbeth is finally convinced and suggests that they further implicate the guards by soiling their daggers with Duncan's blood. This will make all believe that they are the murderers. Lady Macbeth adds that she and her husband will put up such cries of anguish that their supposed sorrow will be proof enough of their own innocence.