I'm confused by your post because there's no such thing as a 'citizen of Northern Ireland' as far as international law is concerned. You're a 'citizen of the United Kingdom of Great Britain and Northern Ireland' and should be treated the same as any other UK citizen. Further, I can find no reference to Northern Ireland on the US embassy website:
http://www.usembassy.org.uk/cons_new/visa/niv/ vwp.html
As long as you've never been arrested for, or convicted of, any offence (excluding minor motoring convictions), you should be eligible for the Visa Waiver Program (which just involves filling out a form on the plane).
If you've ever been arrested (even if you were completely innocent) or convicted, you're not eligible for the Visa Waiver Program and you're required to apply for a visa. This takes at least 5 months. See here:
http://www.theanswerbank.co.uk/Travel/Question 289769.html
In practice, the US immigration authorities don't know about most minor offences, since they don't have direct access to UK criminal records. So many people get in by lying on the form. (If you declared an arrest or conviction when you filled the form in, immigration officials would have no choice but to refuse you entry). However, the UK authorities do pass on some information about convictions, so anyone with a conviction for a serious offence (or posibly even some minor offences involving drugs or sexual misconduct) might get caught out if they tried to lie on the form.
So, if you've led a 'blame-free' life - or if you've just never been caught! - you should have no problems getting into the USA. However, if you've had a 'troubled past', you need to think carefully about whether it's likely that the US authorities would have been made awa