To add search in custom CMS home page just :
Go to the admin under CMS>Pages and select your Home Page. Paste the lines into the Content section wherever you want the search box to appear:
{{block type="core/template" name="home.search" as="homeSearch" template="catalogsearch/form.mini.phtml"}}
to learn more about magento visit : http://www.ilovemage.com/learn-magento-programming-customization-extension-development.html
Thanks