According to Delta Flight Change Policy you should access an official site or mobile application.
The very next thing you need to do is, login to your account with the registered credentials.
With this, you should click on the My trip tab.
After that, you are supposed to enter the confirmation number.
Then, you should mention the First and last name of the ticket holder.
Once, you don with the required details of your booking on Delta Airlines, you should hit the arrow in the red button.
Next, you should choose the trip that you want to change.
Afterward, click on the change option and continue with its prompts as per the instructions visible on the screen.
Lastly, pay the difference and get the notification from the airline to your registered contact details.
Visit: https://www.consult-exp.com/blogs/19401/Do-I-Supposed-to-Pay-for-the-Delta-Change-Flight
Source: https://cancellationflights.com/blog/delta-flight-change-policy/