In order to work in Ireland, I'd suggest having a look at the ressources below.
The Citizens Information Website contains a full section of support for coming to work in Ireland
. For the most current and accurate Passport and Visa advice, I recommend that you directly contact your local Irish Embassy/Consulate
prior to travelling to the Republic of Ireland, and your local British Embassy/High Commission
or Consular Office, should you wish to fly into Northern Ireland.
When it comes to looking for work on the island of Ireland, there are plenty of job sites out there, The main job sites for the Republic of Ireland are Recruit Ireland, Indeed, Monster.ie and Jobs.ie. In Northern Ireland, you have nijobfinder.co.uk, recruitni.com, indeed and jobcentreonline.com.
This should be enough information to get you started.
Best of luck!