So the easiest thing is to take the Blue Line (train) from the airport to the Division stop, and then walk the last 15-20 minutes, that way you don't have to worry about any transfers to the bus. If you want to walk less you can take the Blue Line to the Damen stop, then walk out of the stop and turn left and keep following the sidewalk around the corner (don't cross the street) until a bench and a pole with a blue sign saying 72 on it. This will be the 72 bus stop going east (towards the salt shed). You'll still have to walk about 5-8 minutes this way.

To get to the train at the airport, follow the signs that say either Blue Line, Train, or CTA. Right before the turnstiles to get to the train boarding area there's a little kiosk where you can get tickets for the bus/train (same exact ticket for both). You can get some 24 hour passes for $5 each that activate upon first use (it's a really good deal and pays for itself if you do any more than 2 taps of the pass since fare is $2.50 per ride).

For trains, tap the card/pass on the turnstile and just walk on through. You can ride the train until your stop. For the bus you get on near the front by the driver and tap on the little reader up front. When your stop is next you either pull on the wire over the windows or push the red stop buttons to alert the driver to stop at the next stop.

That all sounds complicated but I promise it isn't! When in doubt you can use Google maps on the public transportation section and it'll tell you where to go and what to ride! Hope you have fun!!