You may be a non-EEA citizen from one of the many countries whereby a visa is not required to visit Ireland, but that doesn't mean you can take up a job to fund your travels while in the country. However, there is a special working holiday visa that you may be able to apply for, and if you receive it, you can have a grand old time enjoying Ireland, while making a few euro along the way.

Ireland has a reciprocal agreement with a list of countries (list below) where 'young' people from both countries can enjoy some time in the other country, while supplementing their stay with some casual work. The intent is not for the applicant to seek a long-term arrangement. 12 months seems to be the maximum stay allowed. (check with your relevant Irish Embassy for official details)

Age Restrictions
As with many things managed by the Irish government, the requirements concerning the applicants age aren't exactly clear. However, the general rule it that the person is 'young' and attending a third level course, or have just recently finished third level education.

Other requirements
According to the Dept. of Foreign Affairs, "you must have enough money to support yourself for at least the first part of your holiday or in case you don’t find work". See what I mean about clarity? I can't tell you exactly what "the first part of your holiday" means, but I imagine that you would need to demonstrate that you have savings to cover a least a couple of months of expenses. You'll need to prove this with bank statements. On the DFA webpage covering this topic for US citizens, it says you need to show you have either €1,500 plus a return travel ticket, or €3,000.

The DFA 'strongly recommends that you get private medical insurance" to cover any illnesses/accidents you have while in Ireland. I actually believe they mean you must have it. This is probably one area you don't want to cut costs. Shop around for a decent multi-month travel insurance policy that covers medical costs while you are in Ireland. It'll be at least worth the peace of mind.

You must register with the Gardai (Irish police force) if you plan to stay longer than 90 days. This is going to set you back €300, so budget accordingly.

It goes without saying (but I'll say it anyway 🙂 ) that you'll need a valid passport, and  to submit an application form. The application form will require various tidbits of information about you, and a fee will be payable too.

List of Eligible Countries
At the time of writing (September 2015) working holiday visas for Ireland area available to citizens of:
Argentina
Australia
Canada
Hong Kong
Japan
New Zealand
South Korea
Taiwan
USA

Last point...
If you weren't already aware, Ireland has a huge student population (a product of free/cheap education), and you'll be up against many of them when looking for employment. Decent paying jobs, with plentiful daylight working hours won't jump in to your arms. You'll most likely have to pound the pavement looking for them, so having a nice little nest egg to tap in to if needed isn't a bad idea. But don't let that dishearten you. Go get it!

Resources: https://www.dfa.ie/travel/visas/working-holiday-visas/

Oh...before I go...I'd LOVE to hear from you if you've ever (or about to) applied for one of these visas. What was your application experience like? How was your time in Ireland? Join us and tell us all about it. Thanks