It's very simple. Take a div and set it's display property to none, then write a javascript function which will set the display property of div to block, then call the javascript function on button click.
<div id="dropdown" style="display:none">
<input type="text" width="100" height="30" />
</div>
Javascript function:-
function ShowDiv()
{
document.getElementById("dropdown").style.display="block";
}
Now call this JavaScript function on button click.
that's it!
Good luck.