I have this HTML - its a button placed at the end of a search box:
<input type="image" name="submit" id="searchSubmit" src="images/searchGif.gif" border="0" />
How do I attach a Controller action to it and what is the VF equivalent of this html?
Use an apex:commandButton with the image attribute set to the URL of the image that you want to display.
You may have to specify the full url to the image, depending on where you're holding the image.
You will then need to create a controller class (or extension, as the case may be), which your page is associated with and declare an action method (return type PageReference), which can then be bound to this button