How does Paul know all this? Because of Abraham. Remember him from way back in Genesis?
Paul explains that the Bible tells us that Abraham believed in God, and because of this, God thought he was a swell guy. Awww.
But God didn't like Abraham because of anything special that he did. It wasn't because he slavishly followed the law and somehow earned God's grace. And it certainly wasn't because he was an awesome juggler (he wasn't). God liked Abraham because Abraham had faith in him. God is pretty big on people putting their faith in him.
Want more proof, Paul asks? Well, just remember that God was cool with Abraham before he was even circumcised. In fact, the main reason that Abraham got circumcised was to mark himself with a sign of his new relationship with God.
So Abraham is basically a stand-in for everyone who has ever believed in God, but has not been circumcised. Gentile-Christians, we're looking at you.
Paul is really clear on this point: like Abraham, no one has to work to get on God's good side. You just gotta have faith.
Really, Paul says, if people could just go around doing nice things and win God's favor, then what would be the point of believing at all?
When God promised Abraham that he would have lots of kids and that he would go on to be "the father of many nations," Abraham didn't doubt God. Sure, Abraham was over a hundred years old. And his wife, Sarah, was pretty much barren. But Abraham still believed it would happen. And you know what? It did. Now that's some strong believing.
So there, Paul says. Faith! Abraham had faith in God's promises. That's all he had to do.
The same goes for everyone else. If someone believes in Jesus—that he died so that our sins could be crossed off God's ledger and that he came back to life so that we could be square with God again—then that person is a-okay by God.