When you arrive at ORD, it is best to take the CTA Blue Line.
It runs every 10 to 15 minutes and costs $1.50 each way with unlimited transfers between train lines. Transfers to the buses cost another $.30.
You will most likely want to get off at the Clark and Lake Station. From there you can transfer to brown, orange, green and red lines.
However, the Clark and Lake station is only 2 blocks from state street, and 5 or so blocks from Michigan Avenue. Walking from there might work depending on where you want to go. If you are going to the museum campas on the lake, trafer to the orange line and get of at Roosevelt.
Go to the following website:
http://www.transitchicago.com/
Do not take a cab unless your destination is off the beaten path. A Taxi to/from downtown will cost at least $25 bucks each way.
Everyone takes the blue line from ORD or the Orange Line from MDW. It is very popular with the flight crews who have crashpads in the city.
Have fun! Tain't no place like the Windy City!
throttlejockey