In Shakespeare's Othello there are three main trials that build the plot of the play. In each of these "trials", Iago though not always the judge tries to be the puppet master. He does this by focusing on each characters fatal flaw.
In the play the three main trails go as follows. First there is Othello's trial were he is being judged by the Duke and Brabantio regarding what happened with himself and Desdemona. The second and main trial is that of Othello judging Cassio, though it is not much of a trial per say because Othello is merely listening to what Iago has to say and does not even confront Cassio. The third and most dramatic trial is when at the end of the play Othello confronts Desdemona for the last time only to find out after he's killed her that Iago had been tricking him all along.
When the play begins we are given Iago and Rodrigo in the street outside of Brabantios window debating if they should tell him what they had heard about Othello and Desdemona. This is where the first trial begins. Iago tells Brabantio that he had been "robbed... of half his soul... by a black ram." (1.3.82-85) Iago bakes sure to word everything he says as best he can, stretching any small truth into a lie but one that would appear true, given the circumstances. In this case Iago says to Brabantio that Othello has kidnapped Desdemona and goes on exaggerated everything he says so that when Brabantio gives his testimony to the Duke It sounds a lot like Iago is speaking. When told to answer to this accusation that he has abused and stolen Desdemona from Brabantio all Othello can say is "that I have ta'en away this old mans daughter, it is most true."(1.3.78-79) This, at least at the time is enough to make some people believe everything that Brabantio has just said because they some evidence for it but none against it. It is thing like this that throughout the play make Iago more and more believable to the characters around him.
The next trial gets a little bit more complicated. It starts off with a long dialogue between Iago and Othello, which begins after they see Casio briskly leaving Desdemona's side as they enter into view. At first Othello thinks nothing of this, but this is when Iagos master plan begins. First Iago realizes that Othello will always act on impulse with whatever information he has. This is one reason why Iago stretches out his opinion of what's going on over an entire conversation. Had he just come out and say it Othello probably would not have believed him. Even if he did this would most likely end up in Othello rushing to confront either Desdemona or Casio thus killing Iagos opportunity to elaborate on the subject in a way that Othello would have to believe him. In this scene Iago repeats a lot of words that Othello says in regard to Casio that alone would be meaning less but he says them in a very suggestive tone implying that there was something more to everything he said about Casio. At the time this is very effective and Iago does make Othello a little more than just suspicious. Though as time passes Iago can find no evidence to back up his case and Othello begins to stop believing Iago even to the point that Othello threatens to kill Iago if he finds out he was lying. At this point Iago was desperate and this was when the handkerchief came into play.
Iago places himself and Casio in a position where Othello cold see them but not vice versa. At this distance Othello can also hear what they are saying as long as they are talking with a full voice. Iago profits from this by making sure that they when he and Casio say Biancas name Othello cannot hear so throughout the whole thing he will think that they're talking about Desdemona. Iago uses this specifically when Casio pulls out the handkerchief. This ends up as enough proof to convince Othello that it was Desdemona that had given Casio the handkerchief and that was the last straw it was time for Othello to confront Desdemona.
This is where the last trial takes place. This one is very short and direct because Othello already had his mind made that he is going to kill Desdemona no matter what. Othello confronts Desdemona while she is alone in her room. He asks Desdemona if there is anything she wants to tell him to try and get rid of her sins. He also says that this would be best for her because his mind is made up and she is going to die anyway. At this point Othello has convinced himself that what he is dong is fully justified because Desdemona will betray other men if he does not go through with it. Desdemona pleads for just one more day but he says that he just cannot grant this and that she must die now. Othello proceeds to suffocate Desdemona in her own pillow and though Othello hated to have to do it he at least feels that she can do no more harm but this all changes when everyone enters the room. After a few short dialogues Othello is informed that Iago had been lying the entire time and Othello proceeds to kill himself.