Shortly after the rumble, Dallas Winston and Ponyboy Curtis head to the hospital to give Johnny the news of the greasers' victory. They find Johnny in worse shape than ever, and after telling Pony to "stay gold," Johnny dies. Since Johnny was Dally's favorite, he is particularly upset, and he takes off. Pony returns home and warns his brothers that Dally's "gonna blow up. He couldn't take it." Moments later, they get a call from Dally: He has robbed a grocery store, and "the cops are after him. We gotta hide him. He'll be at the lot in a minute." The boys set out "on a dead run," but before they can reach Dally, the police get to him first. When the cops corner him, Dally raises his gun--in view of the boys who are coming to his rescue. Pony remembers what Dally has told him:

I been carryin' a heater. It ain't loaded, but it sure does help a bluff.

But the police don't know this, and they fire. "He was dead before he hit the ground. But I knew that was what he wanted... and he always got what he wanted."

Dally died by police fire: suicide by cop.

In this book, Dallas dies by being shot by a whole bunch of police officers.

He has robbed a grocery store and the police are chasing him.  He has a gun (which is probably not loaded) and he points it at the police.  At that point, they shoot him.

It seems clear in the story that Dallas is essentially committing suicide.  When Johnny died, Dally was so sad that he ran out of the hospital and it seems that he went straight out and robbed the store.  After he did that, it seem like he purposely got the police to shoot him.