How does Iago control what happens in the play Othello?

Iago doesn't so much control what happens in the play as
he manipulates the other characters so that events happen the way that he wishes.  The
three characters most affected by his psychological warfare are:  Roderigo, Cassio, and
Othello.

Iago exploits Roderigo's love of Desdemona to
great effect.  He convinces Roderigo to be his front man, taking the fall for his
inflammatory words and announcing to Brabantio that his daughter Desdemona has eloped
with Othello.  He also convinces Roderigo that if he would simple "put money in [his]
purse" he (Iago) could secure him Desdemona's love.   Iago intends to put Roderigo's
purse to his own use.

Next, Iago exploits Cassio's drinking
problem.  Today, we would say that Cassio is an alcoholic, and as such doesn't have much
control over his behaviour when he drinks too much.  Iago fills him up with alcohol,
which leads to Cassio being involved in a barroom brawl, which leads to Othello
stripping him of his position.  This demotion is the cause for Desdemona to spend most
of her stage time pleading for Cassio's reinstatement, which adds fuel to Othello's
jealous fire.

But Iago's most masterful manipulation is the
stirring of Othello's jealousy.  He is most skillful here, seeming to have Othello's
best interests at heart, seeming to be cautioning Othello against the thing that he is,
in fact, encouraging -- the belief that Desdemona and Cassio are having an affair. 
Othello, of course, is inflamed to such a degree that he causes his own demise by
murdering his wife in their bed.

The genius (albeit evil
genius) of Iago is that he doesn't actually cause any of the disastrous events, he is
simply able to manipulate others to do the dirty work.