Iago is an interesting villain. Whereas many of Shakespeare's villains—like Macbeth, Lady Macbeth, Angelo (in Measure for Measure), Tamora (in Titus Andronicus), and Richard III—generally take care of business themselves or directly order someone else to do it, it's not until the last act of Othello that Iago does anything to get his own hands dirty. Even then, Iago gets personally involved only because his plan against Othello goes slightly awry, and he has to step in to sort things out by wounding Cassio and murdering Roderigo in act 5, scene 1. Later, in act 5, scene 2, Iago kills his own wife, Emelia, for revealing his plan to destroy Othello and Desdemona, but this occurs only after his plan has already succeeded. Until then, Iago is content to manipulate others into doing his dirty work.

Iago is a master of insinuation and deception, and he uses those skills to take advantage of other characters' weaknesses and insecurities. Othello is a trusting soul, and Iago insinuates himself into Othello's trust— "I know thou'rt full of love and honesty" (3.3.134), "My friend... honest, honest Iago" (5.2.185). Iago also recognizes that Othello has a dangerously jealous nature, and he insinuates to Othello that Desdemona is unfaithful to him after Othello sees Cassio talking with her and quickly leave the scene when Othello enters.

IAGO. Ha! I like not that.

OTHELLO. What dost thou say?

IAGO. Nothing, my lord; or if I know not what.

OTHELLO. Was not that Cassio parted from my wife?

IAGO: Cassio, my lord! No, sure, I cannot think it,
That he would steal away so guiltylike,
Seeing you coming. (3.3.37-43)

In act 4, scene 1, Iago deceives Othello with a staged conversation with Cassio that leads Othello to believe that Cassio is talking about Desdemona, when in fact Iago and Cassio are talking about Bianca, a prostitute who's in love with Cassio.

Unlike other Shakespeare villains who have clearly defined motives and objectives for their villainy (like wanting to be King of England or of Scotland, for example), Iago seems to lack a convincing motivation for wanting to destroy Othello and Desdemona.

IAGO. I hate the Moor. (1.3.379)

There's a racist motive involved, but it's difficult to know if it's Iago who's racist—he constantly refers to Othello as "the Moor"—or if Iago is simply playing on the prejudices of other characters like Desdemona's father, Brabantio.

IAGO. 'Zounds, sir, you're robb'd! For shame, put on your
gown;
Your heart is burst, you have lost half your soul;
Even now, now, very now, an old black ram
Is tupping your white ewe. Arise, arise!
Awake the snorting citizens with the bell,
Or else the devil will make a grandsire of you.
Arise, I say!

...[Y]ou'll have your
daughter covered with a Barbary horse; you'll have your
nephews neigh to you; you'll have coursers for cousins,
and gennets for germans. (1.1.91-97, 126-127)

Iago was passed over by Othello for the position of lieutenant, and he resents Othello for promoting Cassio instead of him. (1.1.8-33) This has nothing whatsoever to do with Desdemona and seems a rather insubstantial motivation for everything that Iago perpetrates against Othello in the play. Iago also thinks that his wife, Emilia, might have been unfaithful to him with Othello, but Iago doesn't seem particularly upset by that possibility and dismisses it.

IAGO. ...And it is thought abroad that 'twixt my sheets
He has done my office. I know not if't be true;
But I for mere suspicion in that kind
Will do as if for surety. (1.3.397-400)

Later in the play, Iago uses Emilia's supposed infidelity to rationalize his lust for Desdemona and his desire to destroy Desdemona along with Othello.

IAGO. Now, I do love her too,
Not out of absolute lust, though peradventure
I stand accountant for as great a sin,
But partly led to diet my revenge,
For that I do suspect the lusty Moor
Hath leap'd into my seat; ...

And nothing can or shall content my soul
Till I am even'd with him, wife for wife;
Or failing so, yet that I put the Moor
At least into a jealousy so strong
That judgement cannot cure. (2.1.299-310)

Nevertheless, Iago has no deep or profound reasons for his all-consuming hatred of Othello. The few reasons that Iago confides to the audience and to other characters serve only to justify his behavior rather than to support any substantial motivations for his actions.

Quite simply, Iago doesn't need any reason for his malicious, destructive behavior other than his desire to take revenge on anyone who crosses him or gives him even the slightest provocation.

In Othello, Iago is extremely manipulative. Iago is a master at manipulation. Through his mere words, he plants seeds of doubt in Othello. Truly, Iago is subtle in his accusation as he merely suggests that Cassio may be having an affair with Desdemona. No doubt, Iago manipulates the situation to convince Othello that his wife is unfaithful with Cassio. When Cassio and Desdemona are merely talking, Iago leads Othello to the scene. As Othello views the scene, Iago plants seeds of doubt and jealousy in Othello. He uses hesitation as he speaks. This causes Othello to question what Iago is really saying. With Othello's insistence, Iago gives in and expresses his dislike of Cassio and Desdemona talking to one another:

Ha! I don’t like that.

When Othello questions Iago in saying, "What did you say?" Iago begins scheming. Iago pretends to be hesitant in his accusations:

Nothing, my lord.

Artfully and cleverly, Iago is causing Othello to think that Cassio and his wife should not be talking.

When Cassio realizes that Othello is coming, he quickly leaves the scene. Iago uses this moment to make Othello think that Cassio is stealing away because he is guilty of having an intimate talk with Othello's wife. Iago comments about Cassio quickly fleeing from the scene:

I cannot believe
That he would steal away so guiltily,
Seeing you coming.

Later on, Iago uses Cassio's genuine support of Othello to tempt  Cassio to become intoxicated, thus causing him to brawl with Roderigo. Of course, Iago is a master manipulator:

Come, lieutenant, I have
a bottle of wine; and here outside are a number of
Cyprus gents that would happily drink a round to the
health of black Othello.

Although Cassio initially refuses to drink, Iago uses his gift of scheming and talks Cassio into getting drunk.

After setting the scene, Iago moves on to further his evil plot. After Cassio and Roderigo fight, Othello releases Cassio from his position as lieutenant. Iago furthers his devious plan by manipulating Desdemona. Using Desdemona's prime weakness, naivety, Iago puts Cassio up to seeking Desdemona's help in getting his position as lieutenant back.

With the scene set, Othello begins to believe his beautiful Desdemona has been unfaithful with Cassio. Iago realizes Othello's insecurities and benefits by them. Othello is too trusting of Iago. Iago ever so subtly points out that Desdemona is capable of lying:

She deceived her father by marrying you;

Iago is a crafty manipulator. He definitely causes Othello to question Desdemona's integrity. At the same time, Iago assures Othello that he has only discredited Desdemona because of his love for Othello:

I hope you will consider that what I have spoken
Comes from my love;

Iago craftily apologizes for loving Othello too much:

I humbly beg your pardon
Because I was loving you too much.

Convinced of Iago's love, Othello states that he is forever indebted to Iago:

I am bound to you forever.

No doubt, Iago is a master at deceit. Iago is an excellent actor. He is convincing in his false sincerity. Because of Iago's expert manipulation, Othello smothers his beautiful wife.