The first way that Portia helps Antonio, the one that makes all other help possible, is that she disguises herself as a man. This allows her to appear as his lawyer.
She then questions Shylock.
As she does so, she uses a strong knowledge of the law and superior reasoning to trap Shylock: she admits the legal basis of his claim, but analyzes the letter of the law to show that Shylock has to take flesh without taking blood. When he admits he cannot, she ups the stakes on him, arguing that he must be executed if he takes either more or less than that promised pound of flesh.
She then continues by quoting the law, showing that Shylock not only doesn't get the pound of flesh or his original loan, he "deserves" legal punishment: his life is forfeit unless the Duke shows mercy.