In Act 1, some of King Duncan's forces are fighting the Norwegians. Aside from the casualties of this battle, Duncan orders the execution of The Thane of Cawdor for treason. This is ordered in Scene 2 and confirmed in Scene 4.
In Act II, Scene 2, Macbeth kills Duncan, and regrets it immediately afterward:
To know my deed, 'twere best not know myself. (II.ii.92)
It is revealed in the following scene that Macbeth has also killed Duncan's guards. He claims to have done so, thinking they were responsible for killing Duncan. Duncan's sons, Donalbain and Malcolm leave, fearing for their lives. And in the last scene of Act II, suspicion grows that they were responsible for killing Duncan.
In Act III, Scene 1, Macbeth hires murderers to kill Banquo and Fleance (in order to prevent Banquo's heirs from taking the throne). Banquo is killed in Scene 3, but Fleance escapes.
In Act IV, Scene 2, Macbeth has Lady Macduff and her son killed.
In Act V, Scene 5, Seyton informs Macbeth that Lady Macbeth is dead (presumably from suicide). In Scene VII, Macduff's forces (Birnam Wood) meet Macbeth. Macbeth fights a "young" Siward and he kills the Young Siward. In the final scene, it is revealed that Macbeth is dead, slain by Macduff.