There really should be an add character on the character select screen, the SE website and payment process is as difficult as doing anything in-game, it must just be their way of thinking. Need 5 unnecessary steps to do one easy task. Streamline SE! =P
Anyway I am sure others are having issues finding this, please note you will not be charge right now for adding a character. It will remove the $3 fee when you place the order:
1.From your SE Account screen, choose select service from left menu
2.Choose Final Fantasy XIV
3.Choose Options List
4.Top option is Character, click on "Add new options"
5. Show cost (and subtracts it). Hit Add Options
6. Hit Done
6.Choose "one" from the "Please Make a Selection" drop-down.