How does Iago manipulate Cassio after the lieutenant's humiliating dismissal?
After he is dismissed from his position as Othello's lieutenant, Cassio is primarily concerned with his newly-tarnished reputation. Iago, recognizing Cassio's vulnerability and desperation to win back Othello's favor, decides to council Cassio regarding the best way to reconcile with the general.
Iago's advice, when taken at face value, is good; he advises Cassio to seek Desdemona's help, observing that she always goes above and beyond to help someone who asks her to do so:
She is so free, so kind, so apt so
Blessed a disposition, she holds it a vice in her goodness
Not to do more than is requested.
Iago further describes the influence Desdemona has on Othello, and assures Cassio that all will be well if he follows Iago's suggestions.
At the same time, though, Iago plans to tell Othello that Cassio is "too familiar" with Desdemona--an accusation that he knows will inevitably drive Othello into a fit of jealousy. At the end of Act 2, Iago justifies his actions in a soliloquy:
And what's he then that says I play the villain?
When this advice is free I give and honest,
Probal to thinking, and indeed the course
To win the Moor again?
Ultimately, Iago's plan is clearly a manipulation of Cassio--as well as the other characters involved.