Many of the lasting memories from your overseas experience will come from the times you leave your home away from home. Travel within Ireland is relatively cheap and easy, and getting to the European Continent is too. Depending on when and how long you choose to study abroad you may have ample opportunity to do some exploring. There are many ways to get out of town. Here is a break down of travel both within Ireland and abroad.
It is possible to get to any point via bus, train, or ferry. While booking your own independent adventure is exciting, also consider traveling with planned tours. Many times there are international student organizations which organize excursions near and far from your home university. Also, in most Irish students unions, there are travel agents or advisors who will help you get out of town. This makes the logistics of travel easy for you (transportation, accommodation, and some meals are usually included in tours), and it also gives you the opportunity to meet new people and make new friends. Finally, it’s worth noting that Ireland is especially renowned for its walking trails . These trails, which can be found throughout the country, are perfect for walking or bike-riding, and are an excellent way to see the country and visit some of Ireland’s underappreciated tourist sites.
Irish Rail  links the major cities of Ireland, with stops in between at smaller towns and villages. It does not go to every location, but gets close to most inhabited areas. You can often take the train to a destination close to where you want to be and then go by bus the rest of the way.
Train tickets can be purchased from any rail station, or online at Irish Rail. 
Bus Eireann , the Irish national bus system, is similar to the rail system, but more extensive, and taking the bus can be an even cheaper form of transportation. Nearly every Irish town has at least a bus stop with connections to nearby cities. Larger towns have stations from which you can purchase tickets and plan trips.
Student travelers in Europe have varying desires for their travels. Some take part in a whirl-wind, multi-stop, been-there-done-that adventure that offers the most site-seeing possible in the shortest amount of time. Others opt for a more focused tour of a particular region, where rather than concentrating on the most popular spots, they seek out the paths less traveled and take in the full culture of a country or area. Either method of travel can be the right approach for you, or even a combination of two. The key is to decide before you leave what you are up for, and plan according. Not doing so can cost you time, stress, and possibly most importantly, lots of MONEY!
There are several options to get to mainland Europe. The most common and cheapest way is to use a bargain airline. The two biggest are Ryanair  and EasyJet . Watch these websites often, as special offers on selected flights are common, and a good way to help decide where and when to travel!
It is also possible to take a ferry  from Ireland to the U.K. or France. Once there, cheap flights exist, as does the opportunity for train travel (you can even take a train to Paris from London via the “Chunnel”).
Many students believe that the best way to get around is by purchasing a rail pass. This may be appropriate, but it is also important to consider exactly what kind of holiday you would like and where you want to go before you purchase a pass.
However, rail passes are expensive! There is no question about this and no way around it. However, this is where pre-trip planning can really pay off. If you plan to only see a small number of cities, it may be cheaper to forgo the pass and purchase point-to-point tickets as you go. Trains in Europe are generally reasonably priced and reliable, so don’t be afraid to consider this option. Use travel guides or agents to estimate the cost and time tables of individual journeys
If a rail pass is the way to go, the most popular is the Eurail pass . Many travel options are available, including regional passes. Make sure to understand exactly what your train pass entitles you to, and where you can go. There are various other multi-national passes available, for example British Rail  and German Rail . Use travel guides to determine the most appropriate one for you based on cost and flexibility.
Irish Council for International Students  travel page
Failte Ireland  The National Tourism Development Authority
Aer Lingus  Ireland's National Airline
Bus Eireanne 
Irish Rail 
The National Transport Service 
Irish Ferries 
Dublin Transport Office 
USIT  The Irish student and youth travel service