"Knavery's plain face is never seen till used"

Iago is saying that he's only serving under Othello to take advantage of him. Not everyone can be masters and be in charge, and at the same time not all those who are in charge should be leaders. Some masters are too harsh toward their slaves who have done nothing but good. Those are the ones that should be punished. He's saying that the slaves who appear to be faithful and hardworking, are really the ones that are being deceitful and are looking out for themselves.

Iago's reasonings: He wants revenge on Othello for the accusation of sleeping with his wife, being with Desdemona, and not giving him (Iago) the job that he deserves.

There isn't really any hardcore evidence for all of the things that Iago accuses Othello of. Instead, there are the thoughts that Iago has. He thinks all of these things happened, probably because he's just jealous of Othello and blows things way out of proportion. Because Othello supposedly did all of these horrible and awful things to Iago, Iago has every right to do horrible and awful things to Othello.
Iago is just kind of crazy, if you ask me.