Even the following day, because they don't remember saying goodbye, your friends will assume you were with them until the end. "Such a great night!" they'll text you. "So glad you came out!"
The etymology of the Irish Exit is vague. Some call it "ghosting" or "the phantom"; definitions that are clearer in their meaning based on Phantom of the Opera-type connotations.
While nobody can tell you for sure, it appears the term "Irish Exit" is a 20th Century American development - it's nothing to do, say, with famine-era Irish workers skipping out of potato fields early without telling their farmer. It seems an Irish Exit today comes from Irish Americans skipping out early from their weekly obligations - such as church - or, stereotypically, leaving the pub without telling anybody because they're too sloshed to remember common social courtesies.
Now, I love an Irish Exit. I love the freedom of deciding that my night is over, then, two minutes later, being on my way home. I love that I don't get caught up in multiple never-ending conversations. I love that I don't have to deal with awkward people who don't understand social interaction; those who never know if they are supposed to do a kiss, a hug, a handshake, or a wave (and often attempt a cloddish amalgamation of all four upon farewells).
There are also various other reasons for this kind of exit. Perhaps an ex you don't want to see has entered the room. Perhaps you know you're beyond tipsy and you don't want to get into an embarrassing situation. Perhaps you're so drunk you need to vomit, but want to do it in your own porcelain, not somebody else's when all are in earshot.
However, an Irish Exit is not always appropriate. If you're out with one single friend, you can never ghost away without telling them. Rather than being an easy way to end your night without causing a fuss, it's cruel abandonment that will leave your mate confused, worried, and eventually quite angry at you. Ditto if you're with just a handful of people: particularly really close friends. To them, you're not ghosting. You're ditching.
If you're in a medium-to-large group, though, you're probably in the clear to perform an Irish Exit at your leisure. There's no one-size-fits-all strategy to performing this phantom-esque move. You simply finish up your conversation, excuse yourself to go to the loo or for another drink, then slip outside and on your way.
An Irish Exit is easier in the warmer months, because you don't have a coat to grab (an obvious alarm-bell that you're about to ghost). Irish Exits are also easier if you're male, because you likely don't have to retrieve a bag that will give you away, either.
Irish Exiting is not just restricted to parties and bars. You can also ghost away from corporate events (this is actually the ideal way to leave a Tuesday night work function that's going on way too long), barbecues (when other people's kids have reached gremlin o'clock), and even weddings (as long as people are dancing and the cake is cut).
It's not wise to phantom away from dinner parties, tour groups, meetings, or - least appropriate and most offensive - dates. In all situations people will think you're the rudest clown at the circus with no social graces whatsoever.
Alternatively, of course, they might literally assume you died. Avoid this at all costs. Remember this is an Irish Exit; it's not your Last Exit.