You will not be charged any extra duty or VAT on purchases where the duty and VAT has been paid (for example, goods bought in shops and supermarkets) in another EU country, provided the goods are for your personal use.
However, for cigarettes / tobacco / alcohol, there are allowances on the amounts regarded as being for your personal use. If you exceed these quantities, you may have to demonstrate that the goods are for your personal use, or they may be confiscated and/or incur extra duty. You are not entitled to alcohol or tobacco allowances if you are under 17 years old. You should keep any receipts as proof that you have paid duty and VAT.
Additionally, there are limits on importing meat and dairy, amount of cash, and it is forbidden to transport drugs, counterfeit goods and certain protected animal or plant species.
Full details can be found on the Irish Citizens Advice website here.