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 study, live or 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. 

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.

EEA and Swiss nationals do not need an employment permit, except for Bulgarian and Romanian nationals.

NON EU CITIZENS

People from non-EEA nationals countries need a valid Irish entry visa before their arrival. You will also need to register with the immigration authorities.

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.
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 (these can change):

Single-journey visa €60

Multiple-journey visa €100

Transit visa €25

Bringing Pets to Ireland

Dog National Legislation is present in Ireland regarding the importation of pets so as to keep the country rabies free.

A new system is in place within the EU called the Pet Passport System which allows pets to be brought directly into Ireland from low-risk rabies countries.

Certain conditions apply as outlined on the ISPCA website.

Pets traveling from outside the qualifying EU countries will be subject to six months quarantine.

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

Tip

You will find lots of information on Facebook groups. There are groups for most nationalities in Ireland and they will be able to reply to your questions as many of them have gone through the same process before.