Flight
This is the closest airport (around 15-20 minutes from downtown Madison). However, for certain origin cities it can be a bit pricier/impossible to get a direct flight, so it's sometimes more cost effective to either take a connecting flight from Detroit (DTW), Minneapolis (MSP), or Chicago (ORD).
Flight
If you would prefer to fly to Chicago and then take a bus to Madison, there is a bus from ORD to Madison every 1-2 hours which is $38.10/adult and $13/child under the age of 17. The travel time can vary, but expect somewhere around 3-4 hours. It will drop you off at the UW-Madison campus, relatively close to downtown. If you wish to go this route, tickets for the bus can be bought from CoachUSA here: https://www.coachusa.com/