The Chicago train system is called "The L". Tickets are $2.50 per ride and you can download the Ventra app on your phone for easy usage. You can just use Google Maps to figure out which train/bus will take you where!
The bus system also uses the Ventra app. Tickets are $2.25 per ride.
This is mostly for fun, especially if you're going to Chinatown! Tickets are $10 per ride.
Lyft and Uber are the primary apps.