There are a number of events that lead to Duncan's death in the play.
We first see Duncan in act 1, scene 2. He receives news of the battle: Macbeth has defeated Macdonwald. The Thane of Cawdor is a traitor, so Duncan orders his execution and proclaims Macbeth as the new Thane of Cawdor.
In the next scene, Macbeth and Banquo meet the Witches in the woods. They call Macbeth the Thane of Cawdor and claim he will be "King hereafter." Ross comes and delivers the news that Macbeth is indeed the new Thane of Cawdor. The Witches' prophecies are important because after seeing one come true, Macbeth begins to dream of becoming King.
Macbeth writes a letter to his wife about the prophecies. She then hears the news that Duncan will come stay in their castle, which she sees as the perfect opportunity to dispose of him. She convinces her husband to kill the King.
On his way to do so, Macbeth runs into Banquo and Banquo's son Fleance. This encounter reminds Macbeth of the Witches' prophecy that Banquo's descendants would be kings.
There are many events that lead up to Duncan's death. Narrowing them down to seven will depend on whether you consider a character receiving news to be an event or not. You will also need to decide if you are looking at specific events solely in act 2, scene 1 (as detailed in the other answer) or if you are looking from the start of the play (like my overview above). I hope this helps!