At Midway Airport, follow the signs that say "CTA Trains to City." This will take you to the CTA Orange Line Station. Find the Transit Card Vending Machines. Press "Buy New Card" and insert $2.25 into the machine (if you will be coming back the same way before the end of 2013, insert $4.25 for a roundtrip fare). The machine takes coins and paper money (no pennies or half dollars) but does not make change. Then press the big VEND button and a magnetic strip card called a Transit Card will come out.
Do NOT go into the train station. Instead, take the escalators downstairs to the bus terminal. (Ask someone if you're having trouble.) There, board either the 63W West 63rd bus OR the 386 South Harlem bus. Use your Transit Card to pay the fare. The 63W bus will deduct $2.00 from the balance on your Transit Card, the 386 bus will deduct $1.75. The bus will take you westbound on 63rd Street. Get off at Harlem and 63rd.
(The 63W bus goes west on 63rd, but the 386 bus turns south on Harlem.) Scheduled transit time for either bus: 17 minutes.
Walk to the Northeast corner of 63rd and Harlem. There is a bus stop sign by the brown brick building just past the used car lot. Wait there for the 307 Harlem bus going North. Use the same Transit Card to pay your fare. The bus will deduct $.25 from your Transit Card,. Time: About 50 minutes.
Get off the bus in Elmwood Park at Grand Avenue and 76th Avenue. You will see railroad tracks running along Grand Avenue. The Elmwood Park station on the Metra Milwaukee District West Line is tight there. Wait for a train westbound to Bartlett. Pay the conductor in cash on the train. Fare is $4.75. Time is about 40 minutes.
Caution: During the afternoon rush hour on weekdays, not all trains go to Bartlett and you may need to transfer trains at Franklin Park (but only during the peak of the afternoon rush) so check the schedule carefully.
If you put $4.25 on the Transit Card, save it for your return trip to pay the bus fare. (The return bus fare is 25 cents cheaper because the first bus you are boarding is a Pace bus.)
Information, map, and schedule for the 63W and 386 bus:
(The 386 schedule is inside the 63W schedule.)
Information, map, schedule and a video on how to ride the 307 bus:
Information, maps, and station listings for the Metra train:
Full schedule for the Metra Train:
Here is a map of the area around Midway Airport:
Here is a map of the area around the Elmwood Park Metra station: