Bring your passport and e-ticket to the airport. First you need to check-in. Show your passport and e-ticket to the check-in clerk. The check-in clerk will give you your boarding pass.
Next you need to go through security. Give your boarding pass and passport to the security officer. The security officer will check your passport.
Then put your hand luggage through the security check.
When you are boarding the plane, give the flight attendant your boarding pass. Fill-in the arrival card during the flight and give it to the customs officer when you arrive in New York.