There is actually nothing specific to SharePoint here - this will work the same directly in a html page, using a Form web part or a Content Editor web part (CEWP)

<!-- Catch Enter (KeyCode 13) and submit form -->

<div onkeydown=if (event.keyCode == 13) productSearch()>

   <input type=text name=productId id=productId/>

   <input type=button value=Go onclick=productSearch()/>

</div>



<script>

function productSearch()

{

   var url = http://www.link.com/product.asp?= 

             + document.getElementById(productId).value;



   // Open location in current window

   window.location.href = url;  



   // or Open location in new window

   window.open(url);



}

</script>

See window.open documentation for more options when opening a new window