See an accountant--you have overlapping tax years in two different jurisdictions, and you can't possibly sort that out yourself. Your accountant can download the relevent tax forms from Revenue Homepage Redirection for you, and tell you where to sign etc.
Have you got your PPS number yet from the social security office?
Lamzee is right..you will need an accountant..they are used by almost everyone in Ireland, as many payments have to be claimed at year-end, and are not deducted at source, or via council-tax, as in the UK. (refuse- collection and medical costs for example).
Don't worry about the paperwork, as the accountants do all that, and their charges are both tax and VAT-deductible. The VAT threshold is much lower in Ireland..around €36,000 I think, so it is advisable to register. That way, all expenses which incur VAT allow you to offset it against your payment, which will mean you get to keep 21.5% of the cost. The remainder can then be offset against your tax at 41%. It's an attractive system.
You will be required to register your business and VAT liability in the county in which you reside, even if you don't work there. Again your accountant will help you with this part. Once that is all done, just get to work!
JonF is absolutely right in the sense that there are many threads in the Locum Forum regarding tax allowances etc. These are all well worth reading, as the system as a whole is very similar to the UK, and advice given within those threads can be transposed to the Irish system.
Regarding the IPU, I found it an unnecessary expence, so am no longer a member. It stands for "Irish Pharmacy Union", not "Pharmaceutical", and really only represents pharmacy contractors now. It's up to you though..give them a ring and ask how membership will benefit you personally. I did that and it stumped them completely!
Best of luck..and let us know if and when you need more help..that's why we have the Irish Forum!
Best question to ask is 'will you suport me in a dispute with my employer?'
NPA in UK tried to get insurance for locums, but only on professional problems such as errors, and then only so that employers could pass the buck to the locum.
Moral, join the PDA.
johnep