We're happy to have you!
Heres what you do:
First, go to "Edit my Nation", on the Alliance Affiliation scroll-down menu pick "specify other" and type in "UCN Applicant". Then sign up for our forums. In the "Checkpoint" section you will see "Member Applications". In the "How to Join UCN" thread you will find instructions to make a post with the required information (there are instructions there).
Here's the link to the forums:
http://s7.zetaboards.com/TheCommonwealth/index/
You'll be accepted within a few hours.
If you have any more questions or want any more info on the UCN, let Corpius know (on the UCN forums).