As an expat at an Irish university, with experience with institutions in the US and continental Europe, I can say that Irish universities are open to hiring foreigners (and not just TCD and UCD). There are even quite a few expats teaching Irish literature at universities throughout the Republic.
The academic structure is similar (but not identical) to the UK. As was previously noted, the rank Lecturer comes in two varieties: fixed-term, which would be analogous to a VAP position (typically these can be renewable, but see below) and permanent, which is effectively like an Assistant Professor but with tenure.
In terms of how universities operate, it's quite different from the US, so if you get the job there will be a learning curve.
Cost of living is high, but salaries are generally commensurate, but see my qualification below about the recession. Buying a house can be challenging, but rents aren't too bad.
Relocation reimbursement is laughably negligible here, so be warned.
If you like eating out, Ireland is not a good country to live in. With some exceptions, restaurants tend to be both overpriced and bad. Other than that, I find the quality of life to be excellent (but then I'm not too bothered by rain).
In terms of applying, you'll probably need to revise your cover letter. As with the UK, there is much less braggadocio than in the US. I've seen letters from Americans be scoffed at for their pretension. So, tone it down a bit; but of course you do still need to sell yourself.
The hiring process is much simpler than the US. Roughly a month after the deadline for application, a shortlist of 4-6 candidates will be made. The candidates are then invited to the university, usually 2-3 weeks after the short list is announced. They all present and interview on the same day (sometimes it will be spread over two days). This means that you will almost certainly run into at least a few of your competitors. Typically a decision will be made soon after the final interview. So, if you don't hear from them the evening of the interview or the following day, you probably didn't get the job (I found out the night of my interview).
Because universities reimburse travel costs for the interview, I'm not sure how willing they would be to shortlist a candidate from the US for a fixed-term (as opposed to permanent) position. I know that candidates from Europe do get shortlisted for fixed-term jobs, but the cost of a trans-Atlantic ticket might put you at a disadvantage.
Ireland has been very badly hit by the recession and universities are feeling the pinch. When I moved here taxes were surprisingly low for a European country, but that's in the midst of changing now. There are stories of across-the-board hiring freezes at universities:
http://www.irishtimes.com/newspaper/ireland/2009/0402/1224243862485.htmlIt's unclear (yet) if this affects job searches that are already in motion or if it's just for future hires. In any case, it looks like many fixed-term jobs will not be renewed when the contract expires.