<script>
$(function() {
    $("#test_form").find("#submit_button").click(function(){
        if ($.trim($("#test_form").find("#first_name").val()).length == 0 || $.trim($("#test_form").find("#last_name").val()).length == 0){
            alert("Incorrect format!");
        } else {
            $('#test_form').submit();
        }
    });
});
</script>

<form id="test_form" action="/page.php">
    First name:<br>
    <input type="text" id="first_name"><br>
    Last name:<br>
    <input type="text" id="last_name"><br><br>
    <input type="button" id="submit_button" value="Submit">
</form>