How to reduce negative consequence for the person I plagiarized my assignment from?
Whether your friend deserves a grade or not depends whether he was a willing accomplice or an innocent victim.  If he was a willing accomplice, then probably both of you failing the class is the best thing you can hope for (at least for most US universities, where there are consequences besides failing if the professor or TA chooses to report it).  If he was a victim (he did not share his project with you with the intent that you could just copy it), then he certainly merits a grade.

In any case, the proper thing to do is for you to arrange to meet the professor in person, explain the situation, and apologize.  If your friend was a knowing accomplice, both you and your friend should go together.  Then it is up to the professor.