In Othello, how does lago make himself look favorable in others' eyes?

Iago addresses just this question in Act I, scene i.  He
explains to Roderigo (and the audience) the grievence that he has with Othello's preferment of
Cassio over him.  When Roderigo says, "I would not follow [Othello] then," Iago makes it clear
that he follow no one.  He answers, "I follow him but to serve my turn upon him," and "In
following him, I follow but myself."

This confession sets up the
false behaviour Iago will exhibit throughout the rest of the play.  He, on numerous occasions,
finds just the way to behave that will prey upon his victim's weakness and make Iago, at the same
time, appear to be his or her best friend.  Here are some of the ways he makes himself favorable
to others:

• He convinces Roderigo that he has a chance to
  get Desdemona's love, and that he, Iago, is his ally.


• He convinces
  Cassio both to drink too much, and, once that leads to his dismissal, he convinces him to ask
  Desdemona for help.  All this in the guise of being Cassio's
  buddy.


• He convinces Othello, mostly by swearing that it is NOT
  true, that Othello's wife and Cassio are having an
  affair.

In Act I, scene i, not only does he explain the
situation that has led to his desire to "serve his turn" upon Othello, but he states right up
front that he will hide his true feelings and opinions.  He
says:

Heaven is my
judge, not I, for love and duty,

But seeming so, for my peculiar
end.

. . .I am not what I
am.

Iago is able to make himself look
favorable in others' eyes by "seeming" to be full of "love and duty,"  while beneath, he hides
his true intentions.

For more on Iago's "seeming," please follow the
links below.