If your dropdown is something like this:

<select id="thedropdown">
  <option value="1">one</option>
  <option value="2">two</option>
</select>

Then you would use something like:

var a = document.getElementById("thedropdown");
alert(a.options[a.selectedIndex].value);

But a library like jQuery simplifies things:

alert($('#thedropdown').val());

Use the value property of the <select> element. For example:

var value = document.getElementById('your_select_id').value;
alert(value);

<select onchange = "selectChanged(this.value)">
  <item value = "1">one</item>
  <item value = "2">two</item>
</select>

and then the javascript...

function selectChanged(newvalue) {
  alert("you chose: " + newvalue);
}

var dd = document.getElementById("dropdownID");
var selectedItem = dd.options[dd.selectedIndex].value;