In Shakespeare's Macbeth, how do the witches and Lady Macbeth influence Macbeth throughout the play?
The witches and Lady Macbeth are major instigators throughout the play. They push, encourage, or trick Macbeth into committing horrific acts and sealing his own fate, as redemption becomes more and more unlikely. In Act I, the witches appear and provide Macbeth with a first temptation: they tell him that he will be king, among other things. This awakens in Macbeth an underlying or hidden ambition - that is, to kill Duncan, and claim the throne.
When Lady Macbeth reads her husband's letter, and is thus informed of the prophecy, she immediately leaps into action. She persuades Macbeth to kill Duncan. She does this, mainly, by questioning his manly strength, and feeding his desire for power. She also tries to comfort him after the act.
Thus, we can say that Lady Macbeth builds upon what had already been planted by the witches in Act I. In Act IV, they reappear, but in a much different light. Now, they taunt Macbeth; they show him a procession of eight kings, all of which are descended from Banquo; they mock him by showing the (fatherly, manly, and kingly) success of Macbeth's moral foe. Thus, the witches exacerbate Macbeth's growing madness, and push him further toward his doom (that is, into open conflict with Macduff).
What about Lady Macbeth? At this point in the play, she has gone insane. Her death is crushing to Macbeth (see the "Tomorrow and tomorrow" soliloquy), and may well be his "final straw." All that is left for Macbeth to do is face Macduff, about whom the witches had warned him; Macbeth is unprepared, however, as they had declared that no man born of a woman could kill him. Sadly for Macbeth, Macduff was born by Caesarian.
Ultimately, we can argue that Lady Macbeth and the witches instigate both stages of Macbeth's downfall: first, they goad him into killing Macduff, and second, they add to his madness, despair, and insomnia. They are the spark, so to speak, which ignites the bloody action of the play.