I don't believe they charge a change fee, but you will pay what the new fare is. If the new fare is the same as your existing reservation then it will be no charge to change.
They usually do not charge to change a flight and it is very easy to do online! I do this often when I notice a portion of my airfare has gone down. On the website there is an option to change flight and you will need your cf #. It will pull up you ressie and you click on the portion(s) you want to change and it brings you to a screen where you can book your new flights. It will calculate the new fare and tell you if you have a travel credit or owe more due to the difference in fare. The only thing to keep in mind there is a time frame in which you need to travel when making changes. I called SW the 1st time I used this feature and the res agent walked me through the process!