Daughter flying alone from Athens Greece to Newark to Chicago - Need info/advice

There's a bunch of confusion here still, so I'll try to lay out all the steps in more detail.

One note first. Airlines offer an "unaccompanied minors" service, where airline employees will escort your daughter from the time you drop her off to the time she is picked up by an authorized adult. This service is mandatory for children 15 and under on United (which is utterly insane, but I digress), but the policy varies from airline-to-airline. Not all airlines offer this service, and it isn't available on all itineraries, so if your daughter is young, you'll want to check with the airline to ensure she actually can fly alone.

Before traveling

• Ensure your daughter has an ESTA or a US visa if one is required. If she is a US citizen, she needs a US passport to enter the US. If she's a Greek citizen (and not a US citizen), she can travel to the US for up to 90 days on the Visa Waiver Program, but needs to complete the online ESTA form first and pay the $14 fee.

Athens Airport

• Arrive at the airport. Drop off checked luggage at the counter and receive a boarding pass if you haven't obtained one online already.
• Proceed through the security checkpoint
• Go through the Greek exit immigration check
• Go to the gate, wait for boarding, and board the plane at the appropriate time

Fly

• While on the plane, she'll be given a customs declaration form. She'll need this filled out when she arrives at US immigration.

Newark

• Exit the plane and follow the hallways to the immigration area
• Follow the signs depending on whether she is a US citizen or not to the immigration line. There will be people around to ask questions if she is unsure where to go.
• Go through immigration (also called "passport control")
• Continue to the baggage claim (TV monitors will indicate which baggage claim is serving the flight she arrived on). Pick up checked luggage. There should be luggage carts available in this area.
• Take the bags through US Customs, giving them the declaration form completed earlier.
• Go to the baggage drop for transfer passengers (there will be signs). Give them back the checked bags.
• Follow the signs for connecting flights. Depending on the terminal and exactly when the flight arrives, it is possible that she will have to change terminals in Newark. It is also possible that she will not. Either way, there will be TV monitors that list the gate assignments for flights and uniformed staff to help provide directions.
• Go through TSA aviation security
• Walk to the gate, wait for boarding, and board the plane at the appropriate time

Chicago

• Get off the plane. Follow the signs to baggage claim
• Check the monitors to find the right baggage claim for the flight
• Claim baggage
• Exit the airport (no immigration, no customs)

All international arrivals to the US work the same:

• You first go through immigration.
• Then you claim your bags from baggage claim.
• You take your bag through customs and make any necessary declarations.
• Immediately past customs you drop your baggage for your connecting flight.

You only need to talk to someone at the transfer desk if you haven't got the boarding pass for your connecting flight (or if you are delayed in immigration/customs and miss the flight). If you already have the boarding pass, you can go straight to your gate.

I am going to add this as an answer, but it's only a partial one.

Depending on age and other factors your daughter may qualify for "unsupervised minor" treatment. The programs vary a lot depending on age and needs, and it's up to you and the airline to work out the details, but essentially it falls into two categories.

If she is "very young" then she wears a sticker and is assigned a "guardian" from the airline. This flight attendant (usually) will stick with her the entire length of the flight, will give her special attention, will help her though customs and any security checkpoints, and so on. This is basically a baby sitter. On connecting flight they walk the child through the airport and all security "stuff" to their connecting flight. They may hand off the child to a flight attendant on the next leg of the trip.

If she is "young" then she wears a sticker, and special accommodations are made (these apply to very young as well). Most notably she is put on a list and the connecting flights are not allowed to leave without her. Her seat can't be "bumped" and if she gets "stuck" in security the plane has to wait. The security and immigration/customs etc. people are aware of the sticker's meaning and will go out of their way to make the process smooth for her.

It may be worth while (especially if she is under 18) to speak with the airline about these programs. Usually they are called "Unaccompanied minor" or "Young Traveler" programs. Signing up for these will also let you bypass security and pick her up at the terminal, instead of having to wait at the airport exit/baggage claim.

Now, I am saying all this, but make the realization that these programs started "back in a time" when minors traveling on an airplane alone was no big deal. I remember using these when I was as young as 6 or 7. These days people are likely to scream bloody murder if you have a 6 or 7 year old travel alone. Because of that these programs are not as popular as they once were. Also international flights are a bit different then domestic flights and I realize that, but don't be afraid to use these programs. You may be met with a bit of "Oh my god, I can't believe that a parent would let a child travel alone! What a horrible parent." Just power through that nonsense and talk with the airline. They do have a plan and system in place for these types of things, and they really are good at it.

Be aware that there is a cut off for non-direct flights, and there is usually a fee. Unaccompanied minor status is usually valid till they are 18 upon request and usually a requirement until they are 16.

There are some restrictions depending on airline. For example:

https://www.united.com/web/en-US/content/travel/specialneeds/minors/default.aspx

https://www.aa.com/i18n/travel-info/special-assistance/unaccompanied-minors.jsp

https://www.transportation.gov/sites/dot.dev/files/docs/Kids_Fly_Alone.pdf

http://help.jetblue.com/SRVS/CGI-BIN/webisapi.dll?New,Kb=askBlue,case=obj(675)