How and why does Shakespeare create sympathy for Othello?

Othello is human. As we all are from time to time, he is is led astray by false friendships, misplaced trust, and logical fallacies.

The first human and fatal error Othello makes is trusting the evil Iago. Othello calls him "honest Iago," trusting his confidant with the news of his elopement, but Iago plots immediately to betray his friend and tell Othello's father, the Duke.

Othello's judgment fails him again when he disregards his own reasoning, and is swayed by his father's opinion of Desdemona. The Duke plants the idea into Othello's heart that she may be untrustworthy. "Look to her, Moor, if thou hast eyes to see;/She has decieved her father, and may thee" (1.3.291-92.) True, thinks Othello, she *did* decieve her own father...why not me??

This poison seed, wrong from the start, breeds weeds of distrust. How society feels about Othello is the same way any of us may react to such a horrific misplacement of blame. We feel outrage and sorrow, but perhaps also are glad that our own mis-steps did not become so disasterous.

How does Shakespeare use language to create sympathy for Othello?

The agony that Othello endures when he feels that he has lost Desdemona is expressed so eloquently and so passionately that it is difficult not to feel sympathy for Othello even when the reader knows that he is wrong.  Two speeches are particularly poignant.  The first occurs in Act 3 after Iago's words have begun to create suspicion and jealousy:

I had been happy if the general camp,

Pioners and all, had tasted her sweet body,

So I had nothing know.  Oh, now forever

Farewell the tranquil mind!  Farewell content!

Farewell the plumed troop and the big wars

That make ambition virtue!  Oh farewell . . .

In this speech Othello's war and soldier references equate Desdemona's love to all that he feels is important in this world, to all that has defined him as a man. Everything that has made life seem worthwhile is lost to him now that he doubts Desdemona's love for him.

Later, Othello's anguish over the ocular proof Iago has provided of Desdemona's infidelity also reveal his deep emotions.  He wavers between his anger toward Desdemona and his admiration for her in such lines as

Hang her! I do but say what she is, so delicate with her needle, an admirable musician--oh, she will sing the savageness out of a bear--of so high and plenteous wit and invention--

Here, we see Othello expressing within the same sentences his struggle between his love for Desdemona and his belief that she should be punished for her indiscretions.

And of course, Othello's unmitigated remorse for killing Desdemona and his refusal to rationalize his actions also create sympathy for this noble general:

Cold, cold, my girl!

Even like thy chastity. Oh, cursed slave!

Whip me, ye devils,

From the possession of this heavenly sight!

Blow me about in winds! Roast me in sulphur!

Wash me in steep-down gulfs of liquid fire!

O Desdemona! Dessdemona! Dead!

Oh! Oh! Oh!

The heaven and hell imagery here shows Othello's belief that his actions have damned him and that Desdemona's innocence will secure her a place in heaven. The short exclamatory lines indicate his extreme emotion, and the hyperboles show that he  fully understands  that he will suffer not only in this life but in the afterlife.

And finally, Othello's last speech, which places the blame only on himself for throwing "the dearest pearl away" is the last time that treasure imagery is used to describe Desdemona, and shows once more Othello's integrity for admitting his wrongdoing and his willingness to suffer the consequences for his actions.

In this way, pathos for Othello is established.

How does Shakespeare evoke sympathy for Othello in his last speech in Act 5 scene 2?

Othello's last speech is a culmination of his other words in that act-- it is obvious he feels extreme remorse and has realized the error of his ways. He knows his own inglorious death is near and that he has made a monumental mistake. He says:

Of one not easily jealous, but, being wrought,
Perplex'd in the extreme; of one whose hand,
Like the base Judean, threw a pearl away
Richer than all his tribe; of one whose subdu'd eyes,
Albeit unused to the melting mood,

Making the audience understand that he realizes that he has killed something beautiful, and hates himself for it. It's hard not to feel at least a little sympathy for someone who has been manipulated and recognizes the error of his ways. This is a very neat trick, as we've just seen Othello brutally murder Desdemona. The fact that we can now feel sympathy for him is a testament to the power of his speech that emphasizes his own self-hatred.