This is what I did...it was dirt cheap but it took forever.
I took the health sciences bus to get back to the main campus, walked down the street to the train station and then took the train to another some other stop, transferred and took the Airport train. It took forever but it was cheap.
If you have time, you can take the subway(Broad Street line); from Alleghney (the stop next to the dental school) to City hall, then walk to Suburban station and take Regional Rail (R1) to the airport. (should cost about $8 total, but it'll probably take you 45min to an hour to get to the airport) You can check out the schedule online at SEPTA website.
If you are in a hurry, then taxi would be faster (cost about $40-$50, and take about 25-30min).
You can also use airport shuttle services (can check on airport website for the phone numbers). I think it cost about $20, but I never took it before.