If you are new to Ireland and want to buy a car the options for buying a second hand car are either from a dealer or directly from an owner. The advantage of buying directly from an owner is that it will be much cheaper than buying from a dealer. With a dealer the car will be much expensive but some of them give you warranty on the car.
The important points are
1. Make sure the car has an uptodate NCT(National Car Test) which is valid for 2 years from the date of passing. You can't drive a car in Ireland unless it has got an uptodate NCT or exempt from it (Exemption applies only to cars which are younger than 4 years),
2, Don't buy from a dealer unless he/she gives you a warranty since there is no advantage compared to buying from an owner if the dealer does not give warranty and you will only end up paying more. If they give warranty then only it is worth paying more.
3. If buying from an owner it will be a good idea to show the car to a mechanic who will be happy to examine for a fee.