How does Shakespeare represent Macbeth as an ambitious man?

Macbeth is the protagonist of the play and tragic hero, whose tragic flaw is his "vaulting ambition." After Ross confirms the witches first prophecy by informing Macbeth that he has been given the title Thane of Cawdor, Shakespeare illustrates Macbeth's ambitious nature in during an aside. Macbeth says to himself,

If good, why do I yield to that suggestion
Whose horrid image doth unfix my hair
And make my seated heart knock at my ribs,
Against the use of nature? Present fears
Are less than horrible imaginings. (Shakespeare, 1.3.137-141)

Macbeth's violent thoughts and fantasies about assassinating King Duncan reveal his ambition. In act 1, scene 4, King Duncan praises Macbeth for his accomplishments before announcing that Malcolm will inherit the throne. Macbeth once again reveals his ambitious nature by acknowledging that he must also get rid of Malcolm in order to become king. In another aside, Macbeth says,

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. The eye wink at the hand, yet let that be
Which the eye fears, when it is done, to see. (Shakespeare, 1.4.50-55)

After speaking with his equally ambitious wife, Macbeth contemplates assassinating the king and usurping power. In a soliloquy at the beginning of act 1, scene 7, Macbeth weighs his options, thinks about the consequences of murdering Duncan, and gives several reasons as to why he should not kill the king. At the end of the soliloquy, Macbeth reveals that his ambition is the only thing motivating to commit regicide by saying,

I have no spur To prick the sides of my intent, but only
Vaulting ambition, which o'erleaps itself
And falls on th' other. (Shakespeare, 1.7.25-27)

Overall, Shakespeare portrays Macbeth's ambitious nature through his asides and soliloquies, which reveal his inner thoughts and motivation to become king. Macbeth's desire to become king and willingness to assassinate Duncan depict him 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 stepOn 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 spurTo prick the sides of my intent, but onlyVaulting ambition, which o'erleaps itselfAnd 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.