DePaul University's Lincoln Park Campus is conveniently located at the Fullerton CTA El stop. To get to the Fullerton CTA stop from both the airports and/or from Union Station Chicago:
From O'Hare International Airport (ORD): Take Blue Line to the Loop, then switch to the Red Line (toward Howard), the Brown Line (toward Kimball) or the Purple Line (toward Linden), and exit at the Fullerton train stop.
From Midway International Airport (MDW): Take Orange Line to the Loop, then switch to the Red Line (toward Howard), the Brown Line (toward Kimball) or the Purple Line (toward Linden), and exit at the Fullerton train stop..
From Union Station Chicago (CHI): Walk to the Quincy CTA stop (0.3 mile), and then take the Brown Line CTA Train (toward Kimball) or the Purple Line CTA Train (toward Linden), and exit at the Fullerton train stop.
Here is a CTA Train map for your reference.