The best book for control building is Nikhil's Controls book:
Developing Microsoft ASP.NET Server Controls and Components
For what you want to do with a string array, I found this walkthrough that I believe does what you want, step-by-step:
Walkthrough: Serializing Collections of Standard Types with the DesignerSerializationVisibilityAttribute
Hope that helps and Good Luck!
Steven A Smith
President, AspAlliance LLC
CIO, Lake Quincy Media, LLC