If you are travelling to Belfast from Dublin or other city in Republic of Ireland you need known that meazurement units change from Kilometer to Miles and meters to yards, and the signs about distances are different in the same road when you cross the border.
There are no problems driving from the Republic of Ireland into Northern Ireland. There is no discernible border, no stops or checks, so the only indication you have that you are in a 'different' country is that the license plates on the cars are different.You will have to stop and get British Pound Sterling currency, although gas stations and most stores near the border accept British Pounds as well as Irish Punts, with certain adjustments of course. In NI, btw, they will ask to see your passport or ID even if changing US dollars in a bank.This is not the case in the Republic where you can go into any bank and change currency without any questions being asked. Ireland will change over to the Euro on January 1st, 2002, but Great Britain (Northern Ireland) will not be changing.