It’s America’s oldest continuously operating railroad!
ok, how about something useful 
LIRR ticketing occupies the “middle deck” of the dastardly triple layer rabbit warren that is Penn Station: Track level, mezzanine level, Subway track level, street level.
To transfer from Amtrak to LIRR, you have to go up to mezzanine level (which is LIRR tciketing and also Amtrak ticketing level and NJ Transit ticketing level and subway level and shop conscourse level). LIRR has an area near the 7th Avenue side. If you’re at the #2 subway, you’ve gone too far. If you’re at the A/C/E subway, you’re at the wrong end.
In the LIRR area there’s a big line of ticket windows and a bunch of machines that issue tickets. To use the machine, you tell it where you want to go, and it figures the fare and you pay with cash or credit card. The ticket is a credit-card sized slip with your origin destination printed on it. Same thing happens when you talk to a person, actually.
You don’t buy a ticket for a particular train - the ticket is good for any ride between the two points printed on the ticket.
If you are traveling at peak times (6-10am, 4-8pm), you need a Peak ticket. If you accidentally buy an off-peak ticket when you needed a peak, no sweat, you can pay the step-up fare on the train directly to the conductor (its old-timey like that) but only in cash, so have cash if this happens. (pro tip: if you have ANY valid ticket you do not have to pay the on-board penalty just the step-up to the correct pre-purchased fare)
Above the ticket windows is the destinations board where every station in the system is listed alphabetically. Next to each station name is the time the next two trains which stop at that station are leaving. So take note of the train departure time(s) that applies to your destination station. Let’s say you’re going to Forest Hills, on the board the next train is 10:41.
Now turn to your right and see the Train Information Board. There’s a big crowd of people staring at the board so you can’t miss it. Match the time you want to depart to a train line that’s posted as departing at that exact time So you’ll see the 10:32 Port Washington and the 10:41 Babylon. You want that babylon train, the one that leaves at 10:41. Roughly 10 minutes before the train is to leave, the track number is posted. So on the right side of the board the 10:41 Babylon will say “15.” Go to that track, and the train should be there or be about to arrive. they sell booze on the platform from little kiosks. Bizarre! Anyway, get on that train. Sit wherever. Stow your luggage. Do not place luggage on the seats!
After the train leaves the conductor will come around collecting tickets. He or she will punch your ticket (cool fact: every conductor has a unique punch) and may put a slip in your seat saying where you’re getting off in inscrutable code. Conductors will also answer any questions you have. if you’re going past Jamaica (the last stop in City limits) it never hurts to ask if you have to change trains in Jamaica. If there’s no conductor its fine to ask the person sitting next to you. Most people are happy to help.
After leaving Penn Station, the train comes out of the tunnel in Queens and you get a neat view of the skyline if you’re lucky.