You can register a .irish domain name by searching for it using the availability checker on this page. Once your ideal domain shows as available, you can register it (along with other domains if you want).
.irish domains can be registered for annual terms from 1 to 10 years. Once you hold a .irish domain name, you can renew it by adding additional years it any time before it expires, as long as the total period is less than 10 years.