You're not saying which airline they'll be flying with -- but in general practically all airline tickets these days are e-tickets, which means there is no physical ticket and everything happens in the airline's computer system. You book the travel online, specifying the names of the travelers, and then whoever shows up at the check-in desk at the airport and presents a passport in the right name gets to fly.
For flights to the US, the airline will generally want some additional passenger information with the booking, to pass on to the American authorities -- things like dates of birth, passport/visa numbers and where in the US they will be staying. Your friend can provide this information to the airline if she handles the booking process.
Beware that if the ticket is bought directly from the airline using a payment card, some airlines will by default assume that the holder of the credit card is flying too, and will require this particular credit card to be shown at check-in. It should always be possible to avoid this, if you look out for checkboxes stating whether the cardholder is in the group during the booking process. If in doubt, call the airline's customer service and provide them with the 6-character booking confirmation number to make sure the card won't be required at check-in.
It will be useful to forward a copy of the confirmation email from the airline to the sister, so she can bring a printout with her to the airport -- not because she would ordinarily need it to prove she has a ticket (though the information in it might be useful if the check-in agent has trouble finding the right reservation), as much as so she has a reliable record of her itinerary with times and flight numbers.