Here is the simple code change to move search field from magento header to navigation bar.I m using magento 1.4 with default theme.
Go to line no 32 of app/design/frontend/<your -package>/<your theme>/layout/catalog.xml.You will see a code like this
<reference name="header">
<block type="core/template" name="top.search" as="topSearch" template="catalogsearch/form.mini.phtml"/>
</reference>
Change the above code to this
<reference name="left">
<block type="core/template" name="top.search" as="topSearch" template="catalogsearch/form.mini.phtml"/>
</reference>
If this is not working clear you cache by going to system->cache management.Play around with the css to get the proper result.
Nothing To Post 
Better way is to use a “local.xml” file for changing blocks! You have only one place to manage such changes.
You are correct.I haven’t update my post for a while.
Hello,
I’m a newbie. Could you tell me how to move the mini search form from header to the right side under log in ? my homepage is a 1 column page layout..thanks a bunch
Regards,
Celest