Good Friday (the 14th) is a bank holiday but not a public holiday in the Republic of Ireland: most public-transport run normal services, with a few exceptions. However all pubs, hotel bars and off-licenses are closed, all banks and many publc services (eg post-office) are closed, and some other companies treat the day as a "bank holiday".
Easter Saturday and Easter Sunday are not public holidays: usual Sat / Sun timetables generally apply.
Easter Monday is a public holiday, and in most cases Sunday services will be run.
Information from specific bus and train companies is summarised below. Always confirm details with the company.