I just came across this nice MSDN article on ‘Creating a Design for SharePoint 2010 Global Navigation and Search Boxes’. This article has very good step-by-step instructions on how to customize the SharePoint 2010 search box. Recently, my colleague and I spent some time customizing the look of the default search box for a public facing website we are currently working on. Definitely this article would have come handy!
Please checkout the complete article on the MSDN.