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In the film, the Goblet of Fire, Harry is seen waking up at the Weasley residence. But at the beginning of the Order of the Phoenix he is back at the Dursleys'. Why did he go back after running away during the events of the Prisoner of Azkaban?

He didn't run away from the Dursley's (not for good, it was just after that... issue, which was soon before the start of the year in Hogwarts), he's living there even in the beginning of the seventh year. This part of the book was just omitted in the movies.

The first chapter in the book is The Riddle House, which is Harry's dream about Voldemort in the Shrieking Shack. The chapter ends with:

And then the chair was facing Frank, and he saw what was sitting in it. His walking stick fell to the floor with a clatter. He opened his mouth and let out a scream. He was screaming so loudly that he never heard the words the thing in the chair spoke as it raised a wand. There was a flash of green light, a rushing sound, and Frank Bryce crumpled. He was dead before he hit the floor.

Two hundred miles away, the boy called Harry Potter woke with a start.

_{Harry Potter and the Goblet of Fire - Chapter 1 - The Riddle House}

As early as second paragraph in chapter 2, The Scar, you see (emphasis mine):

He sat up, one hand still on his scar, the other hand reaching out in the darkness for his glasses, which were on the bedside table. He put them on and his bedroom came into clearer focus, lit by a faint, misty orange light that was filtering through the curtains from the street lamp outside the window.

_{Harry Potter and the Goblet of Fire - Chapter 2 - The Scar}

and there are no streets with lamps outside the Weasley's. And to prove it, a few paragraphs ahead:

Privet Drive looked exactly as a respectable suburban street would be expected to look in the early hours of Saturday morning. All the curtains were closed. As far as Harry could see through the darkness, there wasn't a living creature in sight, not even a cat.

_{Harry Potter and the Goblet of Fire - Chapter 2 - The Scar}

Chapter 4, Back to the Burrow, tells about the Weasleys' arrival at Privet Drive to take Harry with them:

The atmosphere inside number four, Privet Drive was extremely tense. The imminent arrival at their house of an assortment of wizards was making the Dursleys uptight and irritable. Uncle Vernon had looked downright alarmed when Harry informed him that the Weasleys would be arriving at five o'clock the very next day.

_{Harry Potter and the Goblet of Fire - Chapter 4 - Back to the Burrow}

later on, they arrive:

Loud bangings and scrapings were coming from behind the Dursleys' boarded-up fireplace, which had a fake coal fire plugged in front of it.

"What is it?" gasped Aunt Petunia, who had backed into the wall and was staring, terrified, toward the fire. "What is it, Vernon?"

But they were left in doubt barely a second longer. Voices could be heard from inside the blocked fireplace.

"Ouch! Fred, no - go back, go back, there's been some kind of mistake - tell George not to - OUCH! George, no, there's no room, go back quickly and tell Ron -"

_{Harry Potter and the Goblet of Fire - Chapter 4 - Back to the Burrow}

and by the end of chapter Harry finally leaves the Dursley's:

Harry didn't want to miss the fun, but Uncle Vernon's second ornament narrowly missed his left ear, and on balance he thought it best to leave the situation to Mr. Weasley. He stepped into the fire, looking over his shoulder as he said "the Burrow!" His last fleeting glimpse of the living room was of Mr. Weasley blasting a third ornament out of Uncle Vernon's hand with his wand, Aunt Petunia screaming and lying on top of Dudley, and Dudley's tongue lolling around like a great slimy python. But next moment Harry had begun to spin very fast, and the Dursleys' living room was whipped out of sight in a rush of emerald-green flames.

_{Harry Potter and the Goblet of Fire - Chapter 4 - Back to the Burrow}