The Republic of Ireland is open for work to international applicants. Ordinarily, you would probably need an employment permit to work in Ireland if you are not from the European Union, Iceland, Liechtenstein, Norway, or Switzerland. Also, for permission to reside in Ireland, you need to also register with the Garda National Immigration Bureau.
The Employment Permits system is overseen by the Department of Business, Enterprise, and Innovation. You can apply online and the good thing is that a user guide for the application process is provided. A non-EEA national can now apply for nine different types of employment permits, which can be found on the Department of Jobs, Enterprise, and Innovation (DBEI) website. General Work Permits and Critical Skills are the most common types of employment permits.