I think that the White Witch's manipulation of Edmund is done in three styles.  

The first form of manipulation is addiction.  The White Witch lured Edmund to her sleigh by acting nice and friendly.  She offered him any food that he wanted, and Edmund chose Turkish Delight.  It was the best Turkish Delight he had ever had, and he ate all of it while she quizzed him up and down about his brother and sisters.  The reader is eventually told that the Turkish Delight was magic Turkish Delight that created an uncontrollable hunger for more of it. 

Probably the Queen knew quite well what he was thinking; for she knew, though Edmund did not, that this was enchanted Turkish Delight and that anyone who had once tasted it would want more and more of it, and would even, if they were allowed, go on eating it till they killed themselves.

Essentially Edmund is addicted to the Turkish delight and is willing to do anything just to get another "fix" of it.  

The second form of manipulation is done through temptation.  The White Witch offers Edmund fame, fortune, and power, if he brings Peter, Susan, and Lucy to her.  

"You are to be the Prince and - later on - the King; that is understood. But you must have courtiers and nobles. I will make your brother a Duke and your sisters Duchesses."

Of course Edmund would be tempted with that.  He would get to be king, eat more Turkish Delight, and rule over his brothers and sisters.  Edmund sees that as a win, win, win situation.  

The final form of manipulation is manipulation through fear.  During chapter eleven, Edmund witnesses the White Witch turn a group of forest animals into stone.  The sight terrifies Edmund, but he barely has enough time to consider what he just saw because the White Witch turns and hits Edmund.  She then threatens to do the same to Edmund if he tries to interfere with her again. 

"As for you," said the Witch, giving Edmund a stunning blow on the face as she re-mounted the sledge, "let that teach you to ask favour for spies and traitors. Drive on!"

At the very end of the chapter, she threatens to kill Edmund.  Edmund has no other choice than to obey.  

When Edmund followed Lucy into the wardrobe and thus into Narnia, he encountered the White Witch as Lucy was visiting Mr. Tumnus the Fawn. He was unaware of who she was, that she was the evil queen of Narnia, holding the land in the frozen grips of winter. When the White Witch observed that he was a human, she was reminded of the prophecy of the downfall of her reign at the hands of four humans (two “Sons of Adam” and two “Daughters of Eve”). She manages to manipulate Edmund by first appealing to his greed with a magical batch of Turkish Delight that forced him to keep on eating and not being satisfied when he had finished it off. She also manipulated him by appealing to his pride, promising that he would be her heir, along with his brother and sisters. When Edmund reveals that he does not think much of his siblings, the White Witch uses his resentment by tricking him into betraying Peter, Susan, and Lucy. Too late, Edmund discovers that she does not have grand plans for him after all, making him her prisoner and slave as she searches for the other humans before Aslan the Lion, her arch enemy, can find them and end her control over Narnia.