How does Shakespeare represent Macbeth as an ambitious man?

Shakespeare shows Macbeth is ambitious because he wants to be king even though he has no right to be. 

When Macbeth hears the witches make their prophecies, he has a very different reaction than Banquo does. The contrast between the two men shows how much more ambitious Macbeth is than Banquo. 

Banquo is told that his sons will be king, and he seems not to care. If anything, Banquo is wary of the witches. Macbeth, on the other hand, takes the prophecies at face value and expects them all to come true once the first one comes true. 

When Macbeth is told that he is Thane of Cawdor, which was the witches' first prophecy, he seems to decide every other prophecy must be true, too. King Duncan seems to feel otherwise. He makes the perfectly logical move of naming his son Malcolm successor. Macbeth’s shows how ambitious he really is when he reacts by saying, 

[Aside] The Prince of Cumberland! that is a step
On which I must fall down, or else o'erleap,
For in my way it lies. Stars, hide your fires;
Let not light see my black and deep desires (Act I, Scene 4).

Macbeth is worried about killing King Duncan. You can be ambitious and still be a coward. Macbeth doesn’t have many positive character traits, actually. He goes down the list of reasons why he should not kill Duncan in a soliloquy. In the end, Macbeth determines the only reason he has is that he is ambitious enough to do so. 

I have no spur
To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on the other (Act I, Scene 7). 

Once Macbeth is king, he will do anything to keep it that way. He kills Banquo first because he is worried about Banquo having witnessed the prophecies, including one naming Banquo’s sons king. He then has Macduff’s wife and children killed. There is no end to the bloodshed Macbeth is willing to cause. He brings war to his country just to satisfy his own ambition.