The two major airports in Chicago connect it with rest of the world. Buses and trains can be taken if you are coming from another city in the US.
Air India offers a direct flight from Delhi to Chicago. Other major airlines have connecting flights from all parts of India.
You would be required to obtain a Visa prior to your visit to Chicago. You must contact an American embassy to get the Visa. For further details, follow this link: www.travel.state.gov
O'Hare International Airport is the main airport in Chicago, where most of the international airlines land. The other airport is Chicago Midway International Airport, generally for low-cost carriers.
You can hire a taxi to visit nearby towns from Chicago. Driving on your own is not advisable.
Amtrak provides services to travel to major cities in the US, with a stop at Chicago.
The best way to get around is using "L" (the subway system in Chicago). Other than that, you can take a bus, taxi or Divvy share bike to cover distances. You can ride in a Metro Rail if you're planning to make your way to Chicago Suburbs.