Примерно так:
<div id="borderfx"> </div>
<script type="text/javascript">
function changeBorder() {
document.getElementById('borderfx').style.borderStyle = this.options[this.selectedIndex].value;
}
</script>
<select onchange="changeBorder()">
<option value="solid">Solid</option>
<option value="dashed">Dashed</option>
<option value="dotted">Dotted</option>
</select>