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.