Desdemona loses the handkerchief by accident, it is found by Emilia and she gives it to Iago.
Iago plans on planting it in Cassio's room so it looks like Desdemona gave it to him. This is a part of his plan to get rid of Cassio and drive Othello crazy.
Othello is told that Desdemona and Cassio have been messing around by Iago and starts to lose love for Desdemona. This leads to him hitting her after she continuously talked about Cassio.
Iago than gives Othello the idea to kill both Cassio and Desdemona. He tells Othello to strangle her and then he will kill Cassio. However, he does not actually kill him.
On the other hand, Othello follows through with his plan to kill. After a long drawn out plead and apology from Desdemona (even though she did nothing). He eventually strangles her in their bed. Immediatley feeling regret.
Emilia finds out by walking in on the incident. But she tells Othello that it was all a lie and basically snitches on Iago. Iago walks in then stabs her for snitching on him.
After Othello is shown proof of what actually happened. He decides that he can't live with regret, so he kills himself. THE END