David-
You can add what you described without altering any core code via Javascript.  The trick is to wait until the page has fully loaded, then set the deault value via DHTML and attach your "onclick" event to the search input box.
 
The search input box always has an id of "dnn_dnnSEARCH_txtSearchNew".
 
Here's a post on how to force your Javascript code to wait until a DNN page has fully loaded before executing:
 
  http://www.eguanasolutions.com/DNN_Blog/EntryID/4.aspx
 
And here's a post with an example of attaching an "onclick" event to an already-rendered HTML element (look for the "addeventlistener" section in the sample code):
 
  http://www.eguanasolutions.com/DNN_Blog/EntryID/25.aspx
 
 
You can test out your javascript code using a Text/HTML box.  If you get things working te way you like, transfer the code to you skin.

-mamlin

The quote described adding an empty search box and submit button for DNN search.  This is what you already have with your skin's DNNSEARCH skin object, therefore there'd be a certain amount of coding to do (not much, but some) just to get to where you already are.
 
You described having the box auto-populated with a default value and clearing that value with an event handler for the ONCLICK event.  You'd actually want to clear it when the box gains focus by any means but that's a different topic.
  
If you feel more at ease with replacing the skin object with your own box and code and then adding javascript to that then you can certainly do so.  You'll need to use inline VB in your skin to dynamically determine your portal's Search Results page (so the skin will work in any portal) and then build and attach the results link for your "Search Submit" button.  To build the full search URL you'll need to append the search results page URL with: "?Search={your input box's search term}"
 

My personal preference would still be the JS insert and event attach I first mentioned since you could leverage it for use with any search implementation (see my post on using Google AJAX Search instead of DNN Search) or any type of input box at all whether it's a search box or some other box.  Either method will work, though, and neither should require more than half a dozen lines of code so they should be fairly equal to each other with respect to how much code you have to add.
  
Good luck-
-mamlin