Good Friday (the 14th) is a bank holiday but not a public holiday in the Republic of Ireland: All banks and many public services (eg post-office) are closed, but most public-transport run normal Friday services.
Easter Saturday and Easter Sunday are not public holidays: usual Sat / Sun timetables generally apply.
Easter Monday is a public holiday and a bank holiday, and in most cases Sunday services will be run.
Information from bus and train companies is summarised below. Always confirm details with the company. Bookings are recommended, because there are a number of events happening this weekend.