You could begin with a brief overview of the plot. Background information is necessary. You are to assume the reader may not know the background information of the play Othello.
Your thesis could be that Iago deserves punishment by death. You could write about the reasons Iago deserves punishment by death. After all, he was responsible for the death of Roderigo. He is responsible for the death of Desdemona. He is responsible for the death of his own wife Emilia. How could anyone expect Iago to escape death himself. Iago was an evil character and he deserves punishment by death.
The death penalty is for evil people and Iago fits the definition. He manipulated so many in the play. He cared only about himself. He caused two people who loved each other dearly to lose their marriage--Othello and Desdemona.
Iago destroyed life after life to gain self satisfaction. He was cruel and heartless. Punishment by death is befitting for Iago. If he were to stand trial today, no doubt he would receive the death penalty.
Iago remains to be one of Shakespeare's most evil characters and he deserves the death penalty:
Regardless of the degree to which Iago is to blame for Othello's downfall, he remains one of Shakespeare's most villainous creations, variously described as a brilliant opportunist taking advantage of the chances presented to him, as a personification of evil, and as a stock "devil" or "vice" figure.
Othello give a strange punishment to Iago as he says that
you are a devil and devil never died.