Irish Gaelic is by no means dead, however. It finds its way into the everyday life of everyday Irishmen through a variety of mediums.
The most visible of these are the signs. Most government signs make an effort to be at least bilingual, displaying mixed English and Irish, but it's not uncommon to find all-Irish (or all English) signs throughout the country.
The names you know from Ireland, cities such as Cork, Galway, and Limerick, are all just slightly Anglicized versions of the original Irish names, Corcaigh, Gaillimh and Luimneach respectively. Altered, but the Irish roots still show.
Many Irishmen, even if they themselves can't speak Irish, will still use many Irish words in everyday conversation. For example, the Irish police force, the Garda, retains its Irish name, and people will still use the proper Gaelic pluralization for the word, Gardaí. Another example: the Irish senate is usually referred to by its proper Irish name, the Dáil. Irishmen will ask each other, “What's the craic?”, often misunderstood by other English speakers as crack, to see what's up.
Many Irishmen will also passively listen to Irish Gaelic radio stations and television shows, most popularly the RTÉ Raidió na Gaeltachta but also the government-run Irish television station Teilifís na Gaeilge or TG4 . It's estimated that anywhere between 3 and 8% of Ireland's population use such Irish language media on a daily basis—which isn't enough for many newspapers and radio stations, as more have shut down in recent years than have started up. Many software applications are also available in Irish, from Firefox to certain distros of Linux.
The people themselves still remain proudly Irish, from names like Killian to dancing all night at the Róisín Dubh nightclub to tattooing Éire across the chest to buying a Claddagh heart ring. No, they don't all speak the language, no, they don't all know how to decline for the genitive case or conjugate in the conditional tense—but the spirit of the language is still there.