Airport check-in is free and usually opens 3 hours before departure for flights from destinations outside the US. Delta counters are usually open all day at major airports in America, but many airports have fully automated check-in . You print your boarding pass and baggage tag at the kiosk and then place your bag on the belt yourself.
Check inonline for all flights no earlier than 24 hours before departure. With this option, you can choose to have your e-boarding pass sent to your mobile phone without printing. Just show the barcode at the airport.
Installing the Delta app on your smartphone will speed up the check-in process even more.