One of Ponyboy's most significant actions is when he runs away with Johnny after Johnny kills Bob, the Soc. Johnny does this because the Socs were attacking Ponyboy. They enlist Dallas's help who advises them to hide out in an old abandoned church.
Ponyboy and Johnny tangled with the Socs in the first place because, on Ponyboy's suggestion, they were hanging out in a park late at night when the drunken Socs also turned up. Ponyboy, in effect, had already run away from home after his oldest brother Darry hit him. Ponyboy has a tempestuous relationship with Darry for much of the book. Darry worries about him a lot and gets angry with him very easily in consequence. Ponyboy isn't able to understand why Darry acts as he does, and this precipitates his running away from home.
Ponyboy's running away from home and subsequent hiding-out with Johnny from the law shows that he is feeling lost and miserable and confused. After all he is still very young and he has recently been through the trauma of losing both his parents, and he resorts to desperate measures. He also sticks valiantly by Johnny, his friend and fellow-Greaser. He stays with him even when Johnny urges him to go home:
"This is my fault," Johnny said in a miserable voice. He had stopped crying when I started. "For bringin' a little thirteen-year-old kid along. You ought to go home. You can't get into any trouble. You didn't kill him."
"No!" I screamed at him. "I'm fourteen! I've been fourteen for a month! And I'm in it as much as you are.'
The quote above shows how loyal Ponyboy is to Johnny and the other Greasers. It also shows that, like so many of his age, he is anxious not to be thought of as a mere kid.
Another major action of Ponyboy's is when he, along with Johnny rescues the kids who are stuck in the burning church. He is the one who begins the rescue effort. He proves himself to be brave and selfless when he does this, although it is true he also feels guilty over the fire because he thinks he and Johnny probably started it inadvertently by dropping a lit cigarette while they'd been hiding out in the church.