EU/EEA (The European Economic Area comprises the European Union together with Norway, Iceland and Liechtenstein) citizens and Irish citizens need no work permits.  

If you're from outside the EU/EEA, you will need a work permit, however you can't apply for one yourself unless you are setting up your own business. Your employer has to apply for you, to the Department of Enterprise Trade and Employment.

Find out more about work permits here. 

There is an exception:  if you have particular skills and already have a job offer you can apply for an expedited work permits (a 'working visa') yourself.  The Department of Foreign Affairs provides information about this at http://www.irlgov.ie/iveagh/ under "Travelling to Ireland" link, or you can send email to the Department of Enterprise, Trade and Employment at this address:  workingvisa@entemp.ie

Some nationalities require entry visas as well as work permits. For a list of those who do not require visas (any country omitted from that list will automatically require one to enter the country) please contact the Department of Justice, Equality and Law Reform at immigrationinfo@justice.ie.

For questions on Irish Citizenship, ask your nearest Irish embassy.