RVSM approval is issued by the responsible civil aviation authority. Get in touch with your CAA, they will forward you to the respective person.
Should be no problem online, ie. via email - thats at least how I did it in the past.
Send them all your verfication documents in either an informal application or the standard form, if they use one, pay the bill and get your certificate.
How much depends on your authority. There should be a published catalog of fees what an approval will cost - is usually grouped after MTOW.
Good luck.