Visit Southwest Airlines' "Change Itinerary" page. Enter your confirmation number, and the first and last name of the passenger. Click "Continue."
Check the boxes beside the flight you'd like to change when it is presented to you on the next page. Click "Continue."
Enter the new date and/or time you'd like to fly. Select the most desirable flight from the list of options meeting your criteria. Click "Continue."
Check everything over on the summary page that appears. If your new flight costs more or less, you'll see the difference listed here. Your credit card will either be reimbursed or charged as needed. Press "Submit" to finish the process.