Well, there are many ways to do this. If you want a text field (like the search bar above) then I would try Javascript.
<script type="text/javascript">
function go_to_voice (tag)
{
document.location='http://www.360voice.com/tag/'+tag;
}
</script>
<input type="text" id="gamertag" />
<input type="button" value="Go!" onclick="go_to_voice(document.getElementById('gamertag').value)" />
That should work. Might even be able to simplify it to 2 lines:
<input type="text" id="gamertag" />
<input type="button" value="Go!"
onclick="document.location='http://www.360voice.com/tag/'+document.getElementById('gamertag').value" />
I don't know if the latter will work.