Chicago is served by most major airlines. Most flights arrive at O'Hare International Airport. Some domestic flights (Southwest, ATA) arrive at Midway. Chicago is also a major hub for Amtrak.
From O'Hare Airport (where all International flights arrive) you can take a taxi which will cost about $40, and take from 30-75 minutes depending on the traffic. International flights arrive at Terminal 5, and domestic flights and some from Canada arrive at Terminals 1, 2 and 3. (When you depart make sure to check if you are also leaving from Terminal 5. International Flights on United Airlines and American Airlines, or their code-share partners often leave from terminals 1 and 3 respectively.)
A cheaper alternative than the taxi is to take Continental Airport Shuttle which costs about $19 (check their website for more information, as reservations in advance are sometimes required). Finally you could take the Chicago Transit Authority Blue Line train which costs only $1.50 to get downtown. The nearest stop to the hotel is Clark and Lake, but you would then still need to get a taxi, so this method is not recommended for the weary traveler.