I took a field trip to the airport, so that I could ride back and demonstrate the steps. Google Maps' transit information is quite good, with one caveat below in the Suburban Station section.
Halfway along the walkway to baggage claim, there's a way down to the train platform. There may be an escalator, but it may be going in the wrong direction. There is an elevator and a set of stairs. At the bottom of the stairs, you will see a ticket machine.

You want to Purchase a Quick Trip:

Strangely, you then have to select the only option on the screen. I thought this was an interstitial page and waited for it to clear, but no, you have to pick it:

Your destination zone is Center City Stations:

You will probably pay by credit card (it's $6.75):

At this point I got confused as to what it was waiting for, until I saw the pin pad had a question on it - you may be prompted to enter your zip code:

Your ticket will dispense into this tray below the screen labeled "Fare/Coin? Return"

Here is where Google Maps misled me a little. Please learn from my mistake. I read the map as saying that you should exit towards the front of the train. Boy howdy is that wrong -- in 2 ways:
Instead, proceed towards the rear of the train. This will lead you to the escalator and the lobby of Suburban Station.
You will have to swipe your card at an exit gate. The card is less commonly-used than the proximity "SEPTA Key" card, so there are two possible locations for the card reader - at the top or on the front of the exit gate:


From this lobby, there are clear signs towards the elevator to the street - then walk North along 17th street to the hotel.
There are fare machines in Suburban Station too, and they will sell you a Quick Trip ticket back to the airport. The sequence is slightly different because there are many more destinations from here.
The first screen looks the same, so I didn't take a photo - the Quick Trip is in the lower left. On this machine, there are two screens on which you have to pick the only option:
First, pick Quick Trip Ticket:

Then, pick Regional Rail:

Finally, pick Airport:

Safe Travels!
The content of this page was last updated on 2022-07-23. It was migrated from the old Trac wiki on 2023-01-30.