If you are the listed owner of the domain, you should not have a problem transferring it. In particular, you need to have control of the email address for the admin contact. If you don't have control of this, you've got problems.
Pick another registrar (there are many). Go to the "transfer domains" section of that registrar's site. Proceed with transferring your domain to that registrar. You'll start to receive emails from both registrars asking you to approve the transfer. You'll need to login wherever they say to do this. It should take a few business days for everything to get done.
There are a few squirrelly things that could happen along the way. NSI makes you get an "auth code" which you can only get by calling them. You may also need to access your current registrar's account to "unlock" the domain so the transfer will proceed. You (or your current registrar) may have locked the domain to prevent unwanted transfers.
Exactly what happens depends on who the losing and winning registrars are, because each registrar has a slightly different process.