In Othello, how is Iago's control of Roderigo demonstrated?
Iago uses whatever is within people to manipulate them. What is in Roderigo is lust and a desire to have Desdemona at all costs. Iago works him by convincing him that his money (along with Iago's love) can buy Desdemona, a woman who cannot be bought. Iago exploits Roderigo's prejudice and his passion by continually telling him to "put money in [his] purse" and to follow Desdemona. Once he has turned virtue (love) into vice (pursuit of a legally married woman), Iago is able to continue to manipulate Roderigo into deeper and deeper vice until he has him agreeing to kill a stranger for "love".
We can see the degree of Iago's control first by the fact that Roderigo does sell all of his lands to follow him, second by Roderigo's own admission that he has given Iago enough jewels to corrupt a votarist (a nun) and finally by his constant willingness to put aside his complaints and follow Iago's plans--regardless of how sinister and immoral.
Roderigo is a natural patsy. He is very gullible and easily manipulated by Iago. Iago makes great use of Roderigo's gullibility when he earns Roderigo's loyalty in stating a mutual dislike for Othello.
Roderigo was in love with Desdemona, but Brabantio forbade him to court her. He is devastated to learn that Desdemona had eloped with Othello. Iago uses this too his benefit. Iago is jealous of the power and position of Othello, and he finds it infuriating that he was not given the promotion that went to Cassius.
Iago prompts Roderigo to wake Brabantio with the news of Desdemona and Othello's departure. He is then able to implant insecurities and worries into Brabantio's mind about the dire consequences of Othello and Desdemona's relationship.