Applying for new generic top level domains is not really a regular domain registration but it is application to run and operate new gTLD and that requires some serious technical and financial resources.
If you are still interested of applying for a new gTLD you can do that through the TLD Application System (TAS) that is online submission system for new gTLD applications and that is operated by Internet Corporation for Assigned Names and Numbers (ICANN). You got till 29 March 2012, that is the last chance for new applicants to register and till 12 April 2012 is the last application time.
Application itself is a lengthy process and ICANN has released an Applicant Guidebook for it. I think there is like 50 questions you must answer and lot of requirements and you need to give a deposit of $ 5000 and another payment of $ 180000 must be paid with final application.
Look at this ICANN craft below and you see how complex this registration is, nothing like registering a domain through GoDaddy:
You can read more about registering and applying for the new domain name extensions at ICANN website - New gTLDs: What to Expect in 2012