It is very simple. Create a new module: SearchArea. Delete Sample.txt and Elements.xml. Create a new file: SearchArea.xml

<?xml version="1.0" encoding="utf-8"?>
<Elements xmlns="http://schemas.microsoft.com/sharepoint/">
<Control
Id="ContosoSearchAreaBox"
Sequence="15"
ControlClass="Microsoft.SharePoint.Portal.WebControls.SearchBoxEx"
ControlAssembly="Microsoft.Office.Server.Search, Version=14.0.0.0,
Culture=neutral, PublicKeyToken=71e9bce111e9429c">
<Property Name="GoImageUrl">/\_layouts/images/Contoso/searchbutton.png</Property>
<Property Name="GoImageUrlRTL">/\_layouts/images/Contoso/searchbutton.png</Property>
<Property Name="GoImageActiveUrl">/\_layouts/images/Contoso/searchbutton.png</Property>
<Property Name="GoImageActiveUrlRTL">/\_layouts/images/Contoso/searchbutton.png</Property>
<Property Name="DropDownMode">HideDD\_useDefaultScope</Property>
<Property Name="FrameType">None</Property>
<Property Name="UseSiteDefaults">false</Property>
</Control>
</Elements>
Next add your searcharea module to a site scoped feature.
In the masterpage locate this:
<SharePoint:DelegateControl runat="server"
ControlId="SmallSearchInputBox" Version="4" />
and replace with your brand new search area: