Flight
Chicago has 2 airports, O'Hare (ORD) and Midway (MDW). O'Hare is a massive airport with most airlines offering direct flights from across the US. It's a hub for both United and American, but also serves many Delta, JetBlue, and Southwest flights. Midway is great for domestic flights as it's a bit smaller and also a little closer to downtown. This is a major hub for Southwest and would be our recommendation for our guests coming from Arizona.
Train
The CTA 'L' Trains (and CTA buses) are our preferred way to get around the city. A single ride costs on the trains costs $2.50 while a ride on the buses will set you back $2.25. We suggest buying a 24-hour pass for $5 if you plan on exploring the city before or after the wedding! Blue Line: Our recommendation as the best way to get downtown from ORD, ~40 minutes. Note that this trip is $5 per person but is almost always quicker than using Uber (and much much cheaper). Car traffic between ORD and Chicago can be pretty bad, often taking an hour or more. Orange Line: Our recommendation as the best way to get downtown from MDW, ~35 minutes. Depending on the time you get in, Uber/Lyft is also an option. While it costs more, it usually only takes ~20 minutes to get downtown.
Travel Note
Please DO NOT RENT A CAR! Parking anywhere downtown will run $40+/night and you will not need a car to get anywhere. It's very easy to get most places in the city by foot, public transportation, or a quick Uber/Lyft.