You'll more than likely fly into Ireland but once you land, there's many ways to get get around from cycles, cars, buses and trains. Integrated ticketing as finally arrived in Ireland as has a central body for all transport operators...
If you are located in the Capital, it won't be long until you see long bike racks scattered around the centre especially near train and LUAS stations. These is the very successful Coke Zero Dublin Bicycle scheme.
You can pay per ride but if you are sticking around it's cheaper to buy an annual pass for €20 which allows you to hop on and off as you please (the first 30 minutes of each journey is free).
Transport for Ireland
A central body for all the main travel operators in this country was finally established in 2015. This new website allows you to plan your journey across the Dublin Bus, Bus Eireann, Irish Rail, DART and LUAS networks.
See the Transport for Ireland website.
Monthly and Annual tickets
Public transport operators like many around try to discorage people from paying with cash and instead have a number of pre paid (weekly, month and annual) cards.
A Leap card allows you to hop across town using a variety of public transport operators, full details are on the website.
If you are working you may be able to pay for your monthly/annual travel ticket/Leap card via your payroll meaning you'll save money as it will be deducted before tax. See the Taxsaver website or your HR for more.