By plane
Chicago has two major airports, O'Hare and Midway. Midway is smaller and closer to the downtown. There are many other airports with regional service in the state, including in Springfield, Rockford, Peoria, Bloomington-Normal, and in St. Louis, across the river from Illinois.
By train
Amtrak serves many different areas of Illinois. All routes start and end in Chicago. You can get into Chicago from virtually all directions, east coast and west coast, north and south. There are numerous daily trains to and from Milwaukee and it is reasonably fast and reliable. There is daily service the Empire Builder to/from from Seattle/Portland, Oregon by way of Milwaukee. You can also get in from Washington DC, New York, and Boston on various daily trains. There are many local trains that serve downstate and southern Illinois that also serve long distance locations. Those routes are as follows:
The UP line from Chicago-St. Louis serves Summit, Joliet, Dwight, Pontiac, Bloomington-Normal, Lincoln, Springfield, Carlinville, Alton, and finally St. Louis. There are 4 trains each day, each way. One of those trains that serves this route is the Texas Eagle, and it will bring you into Illinois from San Antonio, Dallas, Arkansas, and Missouri.
The BNSF route from Chicago-Galesburg-Quincy. Only local service serves the Quincy portion of the line. The other service is provided by 2 daily long distance trains coming from either Los Angeles the Southwest Chief or San Francisco via Salt Lake City and Denver the California Zephyr.
The CN route from Chicago-Carbondale has 3 trains each way daily. One long distance train is provided each way daily and will take you to/from New Orleans via Jackson, Mississippi and Memphis.
There is also a daily train to and from Indianapolis with continuing service on certain days of the week to/from Washington D.C. There is regular daily service to/from Washington D.C. via Toledo, Cleveland, Pittsburgh, and Philadelphia.
By car
Illinois is accessed through interstates 39, 90, & 94 through Wisconsin, 74 and 80 through Iowa, 55, 57, 64, 70, and 72 through Missouri, 24 through Kentucky, and 64, 70, 74, 80, 90, and 94 through Indiana