How do I create a similar “search” element to the one in this site?

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Put the image into the span, for example using background-image, then give it a relative position and move it to the left so it overlaps the right end of the search box, for example:
#g-search-button {
display: inline-block;
width: 16px;
height: 16px;
position: relative;
left: -22px;
top: 3px;
background-color: black; /* Replace with your own image */
}
Working example on JSBin