How does Macbeth come to be Thane of Cawdor in Shakespeare's Macbeth?

The Thane of Cawdor is a traitor and Macbeth is promoted to his title.

Macbeth distinguishes himself in battle, and then hears the prophecies of the three witches.  One of these is that he will be Thane of Cawdor.  The other two prophecies are that he will be king, and that Banqo’s sons will be king.  When Macbeth appears at Duncan’s castle, Ross addresses him with his new title.  That is how he finds out...

The Thane of Cawdor is a traitor and Macbeth is promoted to his title.

Macbeth distinguishes himself in battle, and then hears the prophecies of the three witches.  One of these is that he will be Thane of Cawdor.  The other two prophecies are that he will be king, and that Banqo’s sons will be king.  When Macbeth appears at Duncan’s castle, Ross addresses him with his new title.  That is how he finds out he has been promoted due to his recent battle heroics and the downfall of the person who last had that title.

MACBETH

The thane of Cawdor lives: why do you dress me
In borrow'd robes?

ANGUS

Who was the thane lives yet;
But under heavy judgment bears that life
Which he deserves to lose. … (Act 1, Scene 3)

Macbeth doesn’t seem to be too upset that the current Thane of Cawdor has confessed to being a traitor.  He is more interested in the fact that one of the witches’ prophecies came true.  If one came true, can the others be far behind?

Ever since the witches planted this seed in his head, Macbeth cannot be satisfied.  He wants to be king, because he has been told that he will be king.  When Duncan announces that his son will be his successor, which in most circles would be expected, Macbeth is upset.  He wants all of the witches prophecies to come true, or at least those that relate to him.  He doesn't want Banquo's sons to be king!