The third-level education sector in Ireland consists of a Universities, Institutes of Technology, and Colleges of Education.
From School to Third Level - Undergraduate Education
In order to apply for undergraduate education, you have to apply through the Central Applications Office (CAO): http://www.cao.ie/
Post-graduate education includes courses for those who have already graduated from their first third-level course. The options include post-graduate diplomas, masters degrees and PHDs (Doctorates). Applications for postgraduate education are made directly through the college or university you wish to attend.
General Information on Third-Level Education
Local Citizen Information Boards also have useful information about access to third level education http://www.citizensinformation.ie/en/education/third_level_education/