Depending on where you are from, you may need a student visa to study in Ireland. If you are from an EU/EEA country or Switzerland, you do not need to obtain a visa.
There are also a number of other countries whose citizens are exempt from needing a visa, listed on the Department of Foreign Affairs and Trade website. When you arrive in Ireland, you need to register with immigration authorities. If you are from a non-EU/EEA country or one that is not listed, you will need to obtain a visa to enter Ireland. This can be applied for online, via the Irish Naturalisation and Immigration Service.
To apply for the visa, you will need to provide certain documents. These include a letter of acceptance, evidence of medical insurance or EHIC possession, evidence of sufficient funds (currently a minimum of €7,000 per year), two recent passport photographs, evidence of English proficiency, a passport which is valid for six months beyond the end of your course. More information can be found on the Department of Justice and Equality website.