How did Macbeth win the respect of King Duncan?

In short, Macbeth in Shakespeare's play of the same name, wins Duncan's respect and is rewarded by Duncan when, as the "bloody man" or Captain says:

...he [Macbeth] unseamed him [the traitor Macdonwald] from the nave to th'chops,

And fixed his head upon our battlements. (Act 1.2.22,23)

In other words, Macbeth disembowels the treacherous Macdonwald, beheads him, and raises his head on a pole.  Macbeth also repels the Norwegian force that is allied with the Thane of Cawdor, matching Cawdor blow for blow until, finally, Duncan's forces win.

Thus, Duncan assumes Macbeth to be his loyal Thane, and, along with his respect, gives him the Thane of Cawdor's castle and lands.

Ironically, at the close of the play, Macbeth will be the one beheaded for his treachery.