First you should know that click on that button usually does a POST to some urls, passes the data in that form, here is:
<form id="wwmform" name="wwmform" method="get" action="http://web.archive.org/form-submit.jsp" onsubmit="document.location.href='http://web.archive.org/web/*/'+document.getElementById('wwmurl').value;return false;" style="display:inline;">
<input id="wwmurl" type="text" name="url" size="50" value="http://">
<button type="submit" name="type" value="urlquery" class="roundbox5">Take Me Back</button>
</form>
you see the action attribute? That's where the data goes to.
So in python, you may need urllib and urllib2 to encode the data and post it to the target url and then fetch the outcome.
ps: watch out the onsubmit
requestsand you write up the parameters yourself or automate submission by something likemechanize