First, remember that a soliloquy is a speech presented by a character when he or she is alone on stage. These speeches allow the character to address the audience and explain any emotions, feelings, or plans pertinent to the action in the play. When looking in a play for a soliloquy, look for long passages of text usually following other characters exiting the stage.
At the end of Act I scene III the audience sees the first of Iago's soliloquies.
Thus do I ever make my fool my purse;
For I mine own gain'd knowledge should profane,
If I would time expend with such a snipe(395)
But for my sport and profit. I hate the Moor;
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. He holds me well;(400)
The better shall my purpose work on him.
Cassio's a proper man. Let me see now:
To get his place, and to plume up my will
In double knavery—How, how? —Let's see—
After some time, to abuse Othello's ear(405)
That he is too familiar with his wife.
He hath a person and a smooth dispose
To be suspected; framed to make women false.
The Moor is of a free and open nature,
That thinks men honest that but seem to be so;(410)
And will as tenderly be led by the nose
As asses are.
I have't. It is engender'd. Hell and night
Must bring this monstrous birth to the world's light.
In this passage, Iago first lets the audience see his distrust of Othello as well as his belief that Othello has slept with his wife, Emilia. Despite previous actions that made it seem as though her were a friend to Roderigo and faithful to Othello, this important passage lays out Iago's plans for revenge. He plans to trick Roderigo out of his money, trick Othello into believing his loving wide Desdemona has slept with Cassio (or has been "too familiar with his wife"), and lead Othello to ruin. As his scene ends his plan is born and set into motion (or brought into "the world's light."