You can change the order the icons appear by using the arrows to arrange them. Click the edit pencil to select an icon and to change the name, link, or icon image.

To create a new icon click any of the green plus signs. This will bring you to the page below in which you need to enter the NAME, LINK, and ICON CLASS.

The custom icons are created by entering a custom class in the icon class field. Below are a link and an example page of what some of the icons that are offered. 

To see a full list of available icons: http://mk032.monkpreview.com/_assets/fonts/icons/ (substitute your url for http://mk032.monkpreview.com For example, http://www.YOURCHURCHNAME.com/_assets/fonts/icons/)

Resources:

Link List Help Article

Once you have found an icon that you wish to display, simply choose the name to the right of the icon, for example: icon-cloud-sync. And enter this into the field ICON CLASS. Once you hit save this icon should be entered into the bottom "Social Media" field of your site.