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Look up the Ireland immigration laws specific to your country of residence. Research whether you'll need a visa to enter Ireland. Obtain employment in a category that allows you to have a Green Card or other work permit. Apply for a work permit. Register with the immigration authorities. Get Permission to Remain if you wish to retire in Ireland.
Each country has its own set of rules. Information can be obtained through the Irish Naturalization and Immigration Service.  In many cases, a green card or work permit will be required in order to live and work in Ireland. Certain non-EEA citizens will require a visa in order to enter the country. EEA stands for European Economic Area. You can find this information from the Irish Naturalization and Immigration Service at http://www.inis.gov.ie/en/INIS/Pages/check-irish-visa  If you live in a European country, USA, or Canada, you likely don't need a visa. If you need a visa, apply for your visa at an Irish Embassy or Consulate. This visa allows you to seek entry to Ireland, it does not guarantee it. This includes two options: employment that includes a salary of €60,000 or more, or employment that includes a salary of €30,000 or more and is in a "strategically important" occupations. This includes nurses, IT professionals and other highly skilled workers. A full list of these occupations can be found at https://www.djei.ie/en/What-We-Do/Jobs-Workplace-and-Skills/Employment-Permits/Employment-Permit-Eligibility/Highly-Skilled-Eligible-Occupations-List/.  The Department of Enterprise has created a list outlining the positions which qualify. It can be obtained from their website. They can also provide information on work permits. Green cards are not the only employment based permits that allow one to work in Ireland, but they are the highest form. Green cards allow a person to apply for permanent residence in Ireland after two years, unlike other work permits. Other employment based permits include: General Employment Permits, for those with a salary of €30,000 or more in any occupation, and Dependant/Partner/Spouse Employment Permits, for dependents, partners and spouses of those with a green card. This can be done by you or your employer. Green Cards are valid for a period of 2 years and there is a fee of 1,000 euro (approximately 1,440 USD). This fee can be paid by either you or your employer.  Application can be done by filling out the application form found on the Department of Jobs, Enterprise, and Innovation's website. Some of the information you'll be required to include on the application form includes: details about you like your passport information, social security number, and education and work history, and details about your employer like their employer registered number, address and type of business. If your application for a work permit is successful, and you have your visa if you require one, you may travel to Ireland. Once there, you must register for residency with the Garda National Immigration Bureau within 90 days. This must be done in person. The Immigration officer and Garda station can be found in Burgh Quay for those residing in Dublin. Those outside of Dublin should contact their local Garda station to locate the local Immigration Registration Officer.  If you're a non-EEA national, you will be issued a GNIB (Garda National Immigration Bureau) card when you register. There is a €300 fee. This can be waived for spouses of Irish citizens, those under 18, and refugees. If you have a visa or do not require one, and you can prove that you will not be a burden to the state, you can be permitted to reside in Ireland for up to five years, at which time you can renew your permission. You prove you won't be a burden to the state, and that your retirement is legitimate, by showing the immigration authorities certain records such as your bank statements, and previous work permits, if applicable.