Declining an offer should be done in writing and as soon as you accept another position.  This is an important step because it maintains a professional connection in your network.

Sample Email

Dear Ms. Smith,

Thank you for the offer that you extended for a position as a research assistant in the Department of Interior Extension Library.  This offer was very attractive, and I had much to consider in reaching my decision.

You have an impressive organization and there are many aspects of the position that appeal to me.  After much thought, however, I have decided to take a position in the Library of Congress.  Their specialized resources and location in Washington, where my family resides, were the deciding factors in this difficult decision.

I appreciate your interest in me and wish to express again my gratitude for your courtesy and consideration.

Sincerely,

Amir Brown