Train travel in Ireland and Scotland is easy and accessible from most of the cities throughout Ireland and Great Britain. One thing I have learned is booking your ticket far ahead in advance will save you money. You can buy tickets via the internet at Irish Rail for Ireland and the TrainlineUK for Great Britain. If you wait too long and buy at the station it could be double the price. Which I learned on a recent tour there.
Even better is to consider a Rail Pass. The price will be a little more than the individual tickets on the internet, but you won’t be locked into a date. You can just fill in a date when you decide to use it. The Rail Pass needs to be purchased before you leave home. The pass will be mailed to your home address. You can purchase the pass from your travel agent.