The first indication is when Macbeth is informed by Ross that King Duncan had awarded him the title, Thane of Cawdor.
And, for an earnest of a greater honour,
He bade me, from him, call thee thane of Cawdor:
In which addition, hail, most worthy thane!
For it is thine.
Macbeth was in disbelief and asked why Ross was greeting him in 'borrow'd robes' since the Thane of Cawdor was still alive. Ross then informs him:
Who was the thane lives yet;
But under heavy judgment bears that life
Which he deserves to lose. Whether he was combined
With those of Norway, or did line the rebel
With hidden help and vantage, or that with both
He labour'd in his country's wreck, I know not;
But treasons capital, confess'd and proved,
Have overthrown him.
In brief, Ross tells him that the thane of Cawdor lives but that a death sentence had been passed on him for his treason in assisting the king of Norway in his attack against Scotland. He had confessed to capital treason and it is this which cost him his title.
Macbeth, in an aside, sees the announcement as very favorable and believes that the greatest hurdle to his ambition to become king has been overcome. In his and Banquo's earlier meeting with the witches, the weird sisters had greeted him thus:
All hail, Macbeth! hail to thee, thane of Glamis!
All hail, Macbeth, hail to thee, thane of Cawdor!
All hail, Macbeth, thou shalt be king hereafter!
Since the first prediction had come true, Macbeth is confident that the others will also come to pass. He does indeed become king after he has murdered Duncan and his two sons, Malcolm and Donalbain flee to avoid becoming targets themselves. Their disappearance causes suspicion to fall on them for their father's murder. Since Macbeth is closest in line to the throne, being Duncan's cousin, the title is passed on to him and he is crowned at Scone.
Once Macbeth is crowned, he initiates a brutally murderous campaign against all who he suspects of being a threat to his power. He devolves into a bloodthirsty tyrant who spares no one until he is so steeped in blood that he himself realizes that there is no turning back.
In the end, it is his 'vaulting ambition' and gullible belief in the witches' prophecies that lead to his destruction.