Irish grads don't do a "match" per say. It differs in different places. At the moment, each university allocates spots to its graduates at its own teaching hospitals and connected peripheral hospitals. Intern year here right now you do 6 months medicine, 6 months surgery. Which rotations you do during these months depends on your "rank list" of specialties. Getting the ones you want depend on merit (as in the ones who score highest get first pick) in some places. In others, Irish/EU will be placed over non-EU. In the past, each student staying in Ireland could be matched. This year is one of the first years where there is not enough job positions for the number of graduating students. So I'd say for future years, do NOT count on getting a job here, it's not guaranteed.
As in the US, you would apply for residency in your final year. I believe the earliest you can send your applications in to ERAS is around September 15th, so turn in your application in September of your final year. Then you start interviewing November-February, making sure to have all your USMLE steps completed by December (or latest - late January).
For organizing rotations...do them when you can, plain and simple. Some elective programs require Step 1 scores/pass and for you to be in final year having completed all your main core rotations.