I assume you're talking about a permanent export.
I don't know about Ireland as it's a different country to the UK (Northern Ireland is part of the UK though) but as a member of the EU, the principles will be the same. You ship your car out of the US. i did mine ro-ro and it was $820 plus $400 marine insurance. Most countries have import duty which for the UK is 10% of the US purchase price. but if you've owned the car in the US for 6 months (I think) before you export and intend keeping it for at least 12 months after for your own personal use, you don't pay import duty at all.
But you do pay VAT. In the UK, it's 17.5% on the price AND the shipping cost.
Once it arrives in the country, you usually have to pass a test to make the car conform to the country's regulations. In the UK (and probably Ireland too), this involves fitting white sidelights, a rear fog light and switch, side flashers and orange flashers at the rear (usually done by converting the stock reversing lights using orange bulbs and fitting an add-on white reversing light under the bumper. You can usually adjust the headlamps to pass the test (The Single Vehicle Approval test) but this test (at least in the UK) is strict and modified cars would have a harder time getting through it compared to a stock car.
The electrical modifications should be entrusted to one of the companies specialising in SVA work as the (expensive) multi junction box fails if it's not done correctly and you end up with no brake lights or flashers.
Once a car is 10 years old, the SVA doesn't apply and basically you can iumport the car and just submit it for an annual MOT test which is less rigorous but still has to have the mods described.
Once you have the SVA test pass, you can register and tax the car.
Like I say, I don't know how much of the above applies to Ireland and you'd have to research that. It sounds complicated but plenty of people do it.
