How did Macbeth's own ambition lead to his downfall?

Macbeth's ambition was not merely a desire to become king of Scotland but was an overriding ambition, meaning he was not prepared to wait for the normal rules of succession to apply for him to become king. This would have meant King Duncan and his heirs would have to die before Macbeth could even be considered. Macbeth wanted to bypass this tedious and lengthy process. This meant Macbeth had to assassinate all those who would stand in his way, which leads to his downfall.  

Obviously, usurpation of the throne meant Macbeth had to do evil. He was encouraged in this malicious venture by the witches' favorable predictions that he would be thane of Cawdor and "king hereafter." When the first part of their prediction is realized, Macbeth feels confident the second will naturally follow. 

Lady Macbeth also shares her husband's lust for power and urges him to act. Macbeth initially expresses doubt about the success of such a malevolent enterprise, but Lady Macbeth was relentless. She calls him a coward, challenging his love for her and questioning his trust to such an extent that Macbeth eventually gives in. He then says, in the closing lines of Act 1, Scene 6:

I am settled, and bend up
Each corporal agent to this terrible feat.
Away, and mock the time with fairest show:
False face must hide what the false heart doth know.

This decision marked the beginning of Macbeth's descent into ignominy and eventual doom. He and his wife carefully plotted the king's murder, and, once they successfully murder Duncan, Macbeth is crowned king. Malcolm and Donalbain, the king's sons and heirs, fled, which makes them the prime suspects in their father's demise. 

Once Macbeth is king, he becomes paranoid and suspects practically everyone around him. He begins a malicious campaign in which he plans to destroy everyone he believes is a threat. This leads Macbeth to have Macduff's entire family and Banquo killed. 

Macbeth's tyranny was spurred on by the fact that his counsel with the witches made him believe that he was invincible. Through apparitions, the witches told Macbeth,

Be bloody, bold, and resolute; laugh to scorn
The power of man, for none of woman born
Shall harm Macbeth.

Be lion-mettled, proud; and take no care
Who chafes, who frets, or where conspirers are:
Macbeth shall never vanquish'd be until
Great Birnam wood to high Dunsinane hill
Shall come against him (IV. 1. 79-91).

Macbeth takes everything the witches say literally and believes he is indestructible. Later, Macbeth is confronted by reality when he learns Malcolm's troops are moving up Dunsinane hill, camouflaged by branches cut from the trees of Birnam wood, making the wood appear to be moving. When confronted by Macduff, Macbeth learns Macduff was not naturally born; he was 'untimely ripped' from his mother's womb.   

It is then—just before Macduff kills him—that Macbeth realizes he was deceived by the witches' use of equivocation and paradox, and he curses them. The witches made Macbeth believe he is charmed when, in fact, he is as mortal as everyone else.