A valid passport is required for everyone except EU Nationals who can use a valid ID card.

Non EU nationals will find it difficult to obtain legal work in the Ireland and will firstly need a three month tourist visa, and a work permit if intending to find employment. Work permits will prove difficult to come across for non EU nationals without particular work skills.

EU citizens and EEA

EU/EEA/Swiss citizens: If you are from an European Union member state or one of the countries of the European Economic Area or Switzerland, you are entitled to come to work in Ireland. You do not need an employment permit.
In the 27 countries of the European community, a valid National Identity Card or Passport is enough. You don't have to fill any other form in. In many cases, your new company will do the formalities for you.

The 27 countries of the European Union are: Germany, France, The United Kingdom, Spain, Portugal, Austria, Italy, Finland, Ireland, Netherlands, Luxembourg, Belgium, Denmark, Greece, Sweden, Czech Republic, Estonia, Cyprus, Latvia, Lithuania, Hungary, Malta, Poland, Slovenia, Slovakia, Bulgaria, Romania.

Non EU citizens

EEA and Swiss nationals do not need an employment permit, except for Bulgarian and Romanian nationals.
People from non-EEA nationals countries need a valid Irish entry visa before arrived. After, you need to register with the immigration authorities .
The visa issued to you is for a single entry to the State. If you wish to leave the country you must apply for a re-entry visa. Before you can get a re-entry visa you must be registered with the Garda National Immigration Bureau (GNIB). 
The standard non-refundable visa application processing fees are:

Visa Office

Line 1:
Irish Naturalisation and Immigration Service
Opening Hours:
Mon, Wed, Fri 10.00 a.m. - 12.30 p.m.
Tel: + 353 (0)1 6167700
Local: 1890 551 500
http://www.inis.gov.ie
Email: visamail@justice.ie