WordPress Plugin Development Ajax and posting to database/admin email

Solution:

Here’s the jquery I use for that which I usually add to wp_enqueue_script js folder

$(document).ready(function(){

    // grab the submits button ID. do not use <input type="submit"> inside the form. Use a button instead outside the form.
    $("#submit2").click(function()
    {
        // grab the forms ID
        $("#message").submit(function(e)
        {
            // add a loading image in place of your returning outcome
            $("#simple-msg").html("sending...");

            // serialize/combine all submitted fields into an array
            var postData = $(this).serializeArray();

            // set url based of action
            var formURL = $(this).attr("action");

            // set ajax parameters
            $.ajax(
            {
                url : formURL,
                type: "POST",
                data : postData,
                success:function(data, textStatus, jqXHR) 
                {
                    $("#simple-msg").html('<pre><code class="prettyprint">'+data+'</code></pre>');

                },
                error: function(jqXHR, textStatus, errorThrown) 
                {
                    $("#simple-msg").html('<pre><code class="prettyprint">AJAX Request Failed<br/> textStatus='+textStatus+', errorThrown='+errorThrown+'</code></pre>');
                }
            });
            e.preventDefault(); //STOP default action
            e.unbind();
        });

        $("#message").submit(); //SUBMIT FORM
    });

});

I also updated your form with the needed fields, but keep in mind your forms action since you will need to make it point to the page that processes your form

<form name='message' id='message' class="contactusform" method="post" novalidate="novalidate"  enctype="multipart/form-data" action="<?php echo plugins_url(); ?>/your-plugins-name/process.php">
<?php
 if(isset($_SESSION['message']))
 {
 echo $_SESSION['message'];
 unset($_SESSION['message']);
 }
 ?>
     <input type="hidden" name="action" value="add_foobar">
     <input type="hidden" name="data" value="foobarid">
     <label>Full Name:</label><input type="text" name="name" value="" required="">
     <label>Phone Number:</label><input type"=text" name="telno" value="" required="">
     <label>Email Address:</label><input type="email" name="email" value="" required="">
     <label>Town:</label><input type"=text" name="town" value="" required="">
     <label>Device:</label><select name="device" value="" required="">
        <option selected="selected" value=""></option><option value="Not Sure">Not Sure</option><option selected="selected" value=""></option><option value="iPhone 3G">iPhone 3G</option><option value="iPhone 3GS">iPhone 3GS</option><option value="iPhone 4G">iPhone 4G</option><option value="iPhone 4S">iPhone 4S</option><option value="iPhone 5">iPhone 5</option><option value="iPhone 5C">iPhone 5C</option><option value="iPhone 5S">iPhone 5S</option><option value="iPhone 6">iPhone 6</option><option value="iPhone 6 Plus">iPhone 6 Plus</option><option selected="selected" value=""></option><option value="MacBook">MacBook</option><option value="MacBook Pro">MacBook Pro</option><option value="MacBook Air">MacBook Air</option><option selected="selected" value=""></option><option value="iMac">iMac</option><option selected="selected" value=""></option><option value="iPad 1">iPad 1</option><option value="iPad 2">iPad 2</option><option value="iPad 3">iPad 3</option><option value="iPad 4">iPad 4</option><option value="iPad Air">iPad Air</option><option value="iPad Air 2">iPad Air 2</option><option value="iPad Mini 1">iPad Mini 1</option><option value="iPad Mini 2">iPad Mini 2</option><option value="iPad Mini 3">iPad Mini 3</option><option selected="selected" value=""></option><option value="iPod Classic">iPod Classic</option><option value="iPod Mini">iPod Mini</option><option value="iPod Nano">iPod Nano</option><option value="iPod Shuffle">iPod Shuffle</option><option value="iPod Touch">iPod Touch</option>
    </select>
    <label>Message:</label><textarea name="msg" cols="30" rows="4" value="" required=""></textarea>
</form>
<input type='button' id='submit2' value='Send Message' />
<div id='simple-msg'></div>

Hope this helps.