Solo traveller from UK to John F. Kennedy International Airport, NY

Don't worry! Loads of people fly the same route every day, and there are people who can help you at JFK if need be.

Before you travel you should apply via "ESTA" which is like a visa. If your travel dates are fixed, you should apply now, here: https://esta.cbp.dhs.gov/

When you fly from the UK to the US:

1. During flight, you will probably be handed a paper form to fill out. Hopefully you brought a pen! To fill out this form you'll need your passport number, your flight number (on your boarding pass, or ask the crew), and general personal info. There will be some lines asking if you are bringing farm products and other things--for most people the answer to all these is "no." There may also be a question about whether you're bringing more than $10,000 into the country--it'll be easier if you're not!
2. Land.
3. Wait for your fellow passengers to get off the plane, so you aren't squeezed or in a rush.
4. Walk off the plane, into the airport, which will be via a "jet bridge" so entirely indoors.
5. Follow the mass of people toward the signs for "immigration" (or "arrival").
6. There will be multiple queues for immigration. Join one labeled "foreigners" or "other passports" or something like that.
7. The immigration officer may ask you some basic questions, such as how long you will stay. It's a good idea to have a printed copy of your return flight booking in case they ask.
8. The immigration officer will stamp your passport and hand it back to you, along with the customs form you filled out. This is your signal to proceed.
9. Follow the signs to "baggage claim" or "arrival." Wait (typically 10-30 minutes) for your luggage. It helps if you earlier placed some easy-to-see tag on your bag so you know it's yours from a distance when it appears on the conveyor belt.
10. Having collected your bags, follow the signs to exit. Before you reach the doors you will find a small desk with customs officers who will collect your customs form (the same one the immigration officer examined and returned to you earlier). At this point they may ask to search your bags, but probably not.
11. Proceed to the appropriate transportation area--bus, train, taxi, rental ("hire") car, etc. Ignore all unsolicited offers for help once you've left the baggage claim area--there may be the occasional person trying to convince you to let them drive you in their unlicensed taxi.

As for onward travel, there is good, frequent train service to the city if you follow the signs for "subway," "MTA," "trains," and/or "LIRR." The LIRR is the faster train which mostly takes you to midtown Manhattan, but costs more. The subway/MTA takes you to various places at a total cost around 5 GBP (which you will want to have converted to USD before leaving home, for maximum convenience upon arrival).

I just passed through JFK, so I feel qualified to answer.

The first thing that you will encounter upon landing after leaving the aircraft is US immigration.

Your waiting time to be processed can vary from a minute or so, to several hours. If possible, I would avoid stopping to use the toilet, and head straight for the immigration line. If there happens to already be a long line then you can always turn back and return after reliving yourself.

You will have been given a customs form on the plane. Ensure that this is completed because the immigration officer will review and stamp it. He will then return it to you to pass to the customs officer later.

You can expect to be questioned about the purpose of your visit, duration of stay and itinerary. If any of your trip details are yet to be confirmed, that is ok, just be open and honest. However, you should not mention that you are looking for work, or any other activities that would conflict with the declared purpose of your visit.

The immigration officer will then take your photo and fingerprints before officially welcoming you to the United States.

Next stop will be baggage collection. You will need to look at the monitors to identify which belt your baggage will arrive on. JFK is a busy airport, and not the most efficient at getting your bags to you. If you sped through immigration, you may have a 20-30 minute wait before the bags start arriving.

Once you have your luggage then the next stop is customs. You will need to present the stamped customs card to the officer who may or may not further question you. Usually the questioning is on the purpose of your trip and will then become more specific if your answer or demeanour raises suspicion - but really nothing to worry about unless you have breached your duty free limits.

After passing security then look for the signs for ether ground transportation (taxi, limousine, rental car), the subway, or the train. What to take depends on your budget and destination. If you are on a budget then take the subway - it is just as bad/good as taking he underground from Heathrow. I would recommend a separate question for your transportation options.

Returning, then 3 hours should be enough. However note that some of the terminals e.g. BA's terminal 7, have few facilities and are not much fun hanging around (unless you enjoy $10 beers). I would recommend at least 2 hours because security can sometime have long queues.