When you are in edit-mode, each airport will have a trash can icon to delete it, as well as a drag handle. You may reorder your stations in drag-and-drop fashion by dragging them up or down the list using drag handle. If you would like to order your stations alphabetically you may do so by touching the "AZ" icon in the top right corner of the screen. Touch it once to sort your stations alphabetically by their name, touch it again to sort them by their ICAO codes. When you are done exit edit-mode by touching the check mark icon in the top right corner of your screen.
If you have purchased the Groups Add-On and you are in edit-mode each airport will also have a button labeled "Change Group". You may touch it to open a dialog from which you can add or remove this airport to any of your groups at once. Be advised, that in case you remove it from all of your custom groups, it will become part of the group "Not grouped" which contains all your stations that have not been assigned to a custom group. Also be advised, that your airport will always be part of the "My stations" group.