Here is a solution using jQuery:
HTML (note that I added the submit button id):
<form method=post>
<input type="text" id="first_name">
<input type="text" id="second_name">
<input type="submit" value="Submit" id="submit" disabled>
</form>
JavaScript / jQuery:
$(':text').keyup(function() {
if($('#first_name').val() != "" && $('#second_name').val() != "") {
$('#submit').removeAttr('disabled');
} else {
$('#submit').attr('disabled', true);
}
});
Working example: http://jsfiddle.net/nc6NW/1/