What does "I follow him to serve my turn upon him" mean from Othello?
The original question had to be edited down. In terms of Iago's quote, it happens relatively early in the drama. In Act I, it becomes clear that Iago is subservient in rank to Othello, but harbors great anger towards him. The promotion of Cassio over Iago has fueled his anger. The idea of a "motiveless malignancy" is evident in this scene, and while Iago does not fully divulge how this will take form, it does become clear that Iago is going to set in full fruition his revenge on Othello for the wrong done to him.
Shakespeare's use of language in Iago's statement is interesting. The idea of "serve" is one in which there is a master and a servant, one who is subservient to the other. Yet, in this setting, "serve" is used as a way for Iago to be in the position of power, to deliver his vengeance upon another. Iago is following Othello only to bide time so that his revenge can be exacted upon him.
Shakespeare has inverted the idea of serving another, almost to a point where Iago is really serving the master of vengeance within him. It is here where his idea of "follow him to serve my turn upon him" becomes of a clear view into Iago's soul.