Once you get out of the plane and pick up your luggage, walk towards the SEPTA (South Eastern Public Transportation Authority) Terminal. There is a train stop at every airport terminal, and they are very easy to spot with an electronic board announcing when the next train will depart. (There is a train every half hour around the clock.)
If you want to check arrival times at different stations, as well as options for connecting, you can walk over to one of the SEPTA booths located on the ground level of every airport terminal.
Once you board the train, the conductor will start collecting fare tickets or cash and give you a receipt. He will also ask you questions about your destination and help you get there on time, as well as announce every single stop.
You will soon be at the station of your choice after a very stress-free, affordable and comfortable ride.