How do I create a similar “search” element to the one in this site?
If
If you use a background image on the field then there's no way to bind to it to get the click action. So the solution is to have a separate search field and image, so you can bind click event in jQuery to the image. Fiddle here:
http://jsfiddle.net/Lzm1k4r8/23/
You can adjust left:
position to be left or right side of the search box.