How do I turn down an internship offer by a professor because I have a better offer in a corporate research lab?
Just send her/him a polite e-mail saying that although you were/are very much looking forward to working with her/him, you are taking another offer right now, but wish to stay in touch:

Dear Prof. X, I am very much looking forward to working with you.  However, at this time I have also received a placement offer at company Y, and I will go there.  I hope we can work together in the future.
Best regards,
Firstname  Lastname.

Or something similar.  If you are polite and honest, you should be fine.