How does A Doll's House exemlify the theme of manipulation and in what ways?
If by manipulation, you mean "to control or play upon by artful, unfair or insidious means" (Merriam-Webster definition), the only character who really fits this description is Krogstad. He blackmails Nora in Act One out of desperation over potentially losing his position at the bank. He assumes that Nora will be able to influence Torvald in favor of him retaining his position. This is manipulation in the strictest sense of the word, but the idea of Krogstad as a cut-and-dried villain is overturned later in the play when he is reunited with Mrs. Linde.
As for manipulation being a theme that runs throughout the play, there is much deception, false appearance and gender inequality in this play, however I don't know that either Nora or Torvald could be considered to be manipulators. They are, generally, doing what they believe is best for their marriage. Torvald happens to treat Nora in the way that he does, because he sees her as the young, flirtatious girl he married and plans to keep her that way. Nora believes that it is best for Torvald's health (and manly pride) if she keeps her actions secret. But is this manipulation? I don't see the evidence that it is.