How is Macbeth presented as a character who believes in the power of the witches?

There are a couple of ways in which Macbeth is presented as believing in the power of the witches. Firstly, take a look at act 1, scene 3 when the witches deliver their prophecies to Macbeth and Banquo. What Macbeth says to the witches shows just how strongly he values their words and their understanding of the future:

Stay, you imperfect speakers, tell me more . . . Speak, I charge you.

Instead of dismissing what the witches say, as Banquo does, Macbeth encourages them to tell him more, suggesting that he trusts them.
In addition, the fact that Macbeth writes to his wife to tell her of the prophecies also suggests that he believes in the witches' power. If he did not, why else would he mention their meeting to his wife?
Secondly, once Macbeth is king and begins to experience problems with Macduff, he turns to the witches for help. The fact that he goes to them shows that he trusts them and believes in their power to know the future. In fact, based on what he says to Lady Macbeth, we see that Macbeth believes wholeheartedly in their powers of prophecy:

More shall they speak, for now I am bent to know, by the worst means, the worst.