Getting Commits from One Repository to Another

Hi all,

I hope this isn't a FAQ. I searched, and the closest thing in there  
(which may be what I want, but sounded wrong) was "How to share  
objects between existing repositories?" If that is it, then I  
apologize for the bandwidth.

Essentially, when I came on a project, a git repository was made  
available to me (lets call that 'public_repo'). That repository was  
put up on an unfuddle account, as an initial check-in; it was not  
cloned from the repository they were working on (lets call that  
'private_repo'). I wrote some code, and pushed it to the repository.  
Now that I guess they feel comfortable with me, they reveal to me the  
private_repo.

How do I get my code from public_repo to private_repo?

Thanks for helping a novice out.
Ryan