Nihonto Club

Do you mean getting kanteisho ("papers") from NBTHK or NTHK?
I'm aware of two options:
1) Send it to Japan, via a broker. Because the process is so expensive and time-consuming, most folks will also get a polish. BTW, getting a kanteisho REQUIRES a decent polish, so if your blade is not in great condition, you'll have to get a polish first anyway.
2) Sometimes at a major sword show in the U.S. there are people qualified to write a kanteisho.

I don't know the actual cost for any of this.

Showing your blade to a very experienced collector might be "free", and you will likely learn more, although you won't get a fancy paper... :-)

Pete