Being American, depending on the type of job your best chance is with NCL for the Pride of America. I know that they every so often do recruiting events around the country. That is how my grandson was hired by them. He is now on his second contract. Check your newspaper website and any major sites that post job listings. He found out about the recruiting online.
And as Trip said each line has a section on their website.
Caribbean Trip Reports
Star Princess 2005, Sun Princess 2005
Caribbean Princess 2006, MSC Lirica 2006 , NCL Pearl 2007, Majesty of the Seas 2008, Carnival Destiny 2008, MSC Lirica 2009, Carnival Valor 2009,Carnival Legend 2010, Carnival Liberty 2010,Carnival Fantsay 2011,Carnival Valor Feb 2012, MSC Poesia Dec 2012, MSC Poesia April 2013, Carnival Legend Nov 2013, MSC DIVINA Jan 2014, MSC Divina Oct 2014
You might also want to try a recruitment agency. I applied to Seven Seas Group who were great and got me a job on Royal Caribbean. Just make sure you read loads of information online so you know what job you want to apply for, what the job entails and whether you think ship life is for you. Good luck!
While I was always quite skeptical of the online e-books, I took a chance on this one and overall I think it is worth it. There are resume examples, cover letters, info about the different lines, job descriptions, salary ranges, and more. But even more valuable is Earl's willingness to email with you and his very valuable advice.
I'm not at all related or invested in his project, but I think it's worth mentioning here that it is quite valuable.