Check traffic using Google Maps before you leave. As said before, avoid passing through during rush hour if possible. Here are my guidelines when I am going around the city.
Option 1: Take I-80 to the Tri-State Tollway (I-294). Then take I-290 to I-90W (look for signs for Rockford). On I-290 stay to the right side. The road will divide into local and express lanes when you get near I-90.
Option 2: Stay on I-80 until you get to I-355. It will merge with I-290. Take I-290 to I-90 West as above.
Option 3: Take I-80 to I-39N, which will go straight to Madison. This is significantly longer but it avoids Chicago area traffic.
Expect a lot of trucks on I-80. If you don't have an I-Pass, consider getting one. Tolls are doubled for vehicles without one.
Enjoy Madison. It's a great city.