There were two stages to Quirrell association with Voldemort.
Stage 1: Following Voldemort's order
When Quirrell tried to rob the Sorcerer's Stone from Gringotts, he had fully in control of his body. This can be gauged from the fact that he could touch Harry Potter.
“Professor Quirrell!” said Hagrid. “Harry, Professor Quirrell will be one of your teachers at Hogwarts.”
“P-P-Potter,” stammered Professor Quirrell, grasping Harry’s hand, “c-can’t t-tell you how p- pleased I am to meet you.”
Harry Potter and the Sorcerer's Stone, Chapter 5, Diagon Alley
But after he failed to steal the Sorcerer's Stone from Gringotts, Voldemort took control of Quirrell.
Quirrell shivered suddenly. “He does not forgive mistakes easily. When I failed to steal the stone from Gringotts, he was most displeased. He punished me... decided he would have to keep a closer watch on me...”
*Harry Potter and the Sorcerer's Stone, Chapter 17, The Man With Two Faces
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Stage 2: Carrying Voldemort around in his head and following Voldemort's order
This stage mostly started just before Quirrell came to Hogwarts to teach. It involved him performing various tasks like drinking unicorn's blood, jinxing Harry's broom, letting the troll inside Hogwarts, and attempted robbery of the Sorcerer's Stone.
“See what I have become?” the face said. “Mere shadow and vapor... I have form only when I can share another’s body... but there have always been those willing to let me into their hearts and minds... Unicorn blood has strengthened me, these past weeks... you saw faithful Quirrell drinking it for me in the forest... and once I have the Elixir of Life, I will be able to create a body of my own... Now... why don’t you give me that Stone in your pocket?”
*Harry Potter and the Sorcerer's Stone, Chapter 17, The Man With Two Faces
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It was not like Voldemort was in complete control of Quirrell's body. Quirrell could think on his own and could resist Voldemort a bit. But in the end Voldemort got the tasks done his way.
Quirrell came back out from behind the mirror and stared hungrily into it. “I see the Stone... I’m presenting it to my master... but where is it?”
“But I heard you a few days ago, sobbing — I thought Snape was threatening you...”
For the first time, a spasm of fear flitted across Quirrell’s face.
“Sometimes,” he said, “I find it hard to follow my master’s instructions — he is a great wizard and I am weak —”
“You mean he was there in the classroom with you?” Harry gasped.
*Harry Potter and the Sorcerer's Stone, Chapter 17, The Man With Two Faces
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