An American company has opened an office in Ireland and I have been offered a position in the Irish office.
However before I could take up this job, I would need to go to American to get trained in the position, training would probably take approximately 6 months (maybe even less). The full time position is in Ireland and I would be dealing with trade shows etc but as I have never worked in the area of the specified job been offered I would need to be trained over in the American office.
Do you know if it is a H3 visa that we would need to apply for?
Congratulations on the job offer!
An H-3 Trainee visa is definitely one possibility for a training program, and you and your potential employer should seek the counsel of an immigration attorney to ensure that the H-3 is feasible and to see if it is in fact the best fit.
Whether this is viable depends on how the company envisions the program being structured (it would need to have a very substantial classroom curricular component as opposed to consisting of "on-the-job" training - only incidental product work is permitted), the company's ability to sustain such a program, the future benefit to your career, lack of availability of training in your home country, impossibility of learning materials to be trained on through graduate education, and several other factors.
Another possibility might be the J-1 Exchange Visitor Visa. These are also often useful for limited-duration training. With the J-1 various quasi-private entities, often non-profits, are empowered by the U.S. government to run their own programs for training in various areas and issue the paperwork required to obtain the necessary visa at the consulate abroad -so we would apply to them rather than to USCIS, often with a slight time savings.
Each option has advantages and disadvantages, and "quirks" or specific needs unique to your and the company's circumstances might make one or the other a better option - so speak with an immigration attorney to determine what works better given what you both are seeking to accomplish and what your constraints and requirements might be.