By Air
For those travelling by air, Madison is served by the Dane County Regional Airport that connects to several major airline hubs in the US. The downtown/campus is only 20 minutes from the airport by taxi. See details about ground transportation from the airport to the downtown/UW-Madison campus. Uber service is also available in Madison.
The Chicago's O'Hare International airport (ORD) is ~150 miles to the South East of Madison. Those flying in to ORD can choose to rent a car at the airport and drive to Madison OR take advantage of the hourly Van Galder bus service between the airport and Madison.
By Bus
Those planning to take the bus : From Chicago O'Hare, take the Van Galder Bus from either the (international) Terminal 5 (lower level/arrival area) or the Bus Center (in the main parking garage between terminals 1, 2 and 3) in front of the Hilton hotel. The trip to Madison is ~3 hours. The bus departs daily about every hour between 6 a.m. and 11 p.m., and costs ~$30 each way. The last stop is on UW campus. From there you can take a taxi ride to your hotel.
There are also buses from Downtown Chicago run by Van Galder (Coach USA) and Mega Bus.
Find more information on traveling to Madison here.
From the hotels not in downtown
City bus service is available from many places. Driving is possible but requires paid parking at the Monona Terrace. There is plenty of space, so there should be no need for reservations.