Communication is the key. I believe Othello should have communicated with his wife initially. In the very beginning, the two of them could have talked everything out. Then, they could have turned the tables on Iago.
Othello should have gone to Cassio. He could have learned that he found the handkerchief. He could have begun asking questions early on, rather than allowing his jealously to lead to rage.
Another point to consider is why would Cassio be so careless with Desdemona's handkerchief? If he were having an affair with her, he would have concealed the handkerchief. He would never have given it to his mistress Bianca. He would have returned it to Desdemona if he were having an affair with her. Othello should have really considered this fact.
When Othello did decide to talk about it, it only took one conversation with Emilia to learn that Iago had planted the handkerchief on Cassio:
O you stupid Moor! That handkerchief you speak of
I found by luck and gave it to my husband;
Because, he begged me to steal it
Often with a solemn earnestness,
More than, indeed, belonged to such a trifle.
Only one conversation, two minutes of Emilia's time, and Othello knew the truth. Of course, he waited too late. By this time Desdemona was dead.
It is always best to ask questions. Never trust anyone, especially not someone who has been spying. Othello should have been suspicious of Iago. How did Iago know so much about Desdemona and Cassio? Why did he care? Othello should have questioned his motives. Othello should have communicated with his beloved Desdemona before his jealousy was out of control.