There are two major airports in the city of Chicago: O'Hare International Airport (located to the North of downtown area) and Midway Airport (located West-Southwest from downtown). Both airports are accessible by CTA train lines to/from downtown.
Several expressways are merging in the Chicago loop, near downtown (I-90; I-94; I-290; I-55), with a few more merging into other expressways a few miles outside the loop (I-57; I-88; I-294; I-355).
The Central and AMTRAK train stations are also located close to the downtown area.
Within the city of Chicago there are several taxi companies, and the public transportation is managed by the CTA (Chicago Transit Authority) providing numerous bus lines and 7 different train lines.
More detailed information and maps (with links to more detailed info) are available at Chicago Travellers Wiki.