Handling input using PHP and AJAX

I have been trying to figure out this assignment and I really need help. I am really close but but I am stuck on the database part. This is the assignment:

Build a small phone book app that will allow you to create and delete people.

The front end should be a simple page with an interface to create a new person. The interface should have three fields, first name, last name, and phone number plus a submit button. There must also be a list of people. The list should be ordered by last name in ascending order, it should also contain a delete button that removes the user. The delete button should be on the right side of the list, and the list should alternate background colors depending on odd/even.

Javascript should handle basic form validation and all saves/deletes should be done via AJAX.

PHP should handle retrieving all people, adding and removing people from a database.

This is what I have so far for the HTML portion:

<div class="contact_wrapper">
    <ul id="responds">
        <?php
        //close db connection
        $mysqli->close();
        ?>
    </ul>

    <div class="form_style">
        <input name="firstname_txt" id="firstnameText" cols="45" rows="5" placeholder="First Name" required></input>
    </div>

    <div class="form_style2">
        <input name="lastname_txt" id="lastnameText" cols="45" rows="5" placeholder="Last Name" required></input>
    </div>

    <div class="form_style3">
        <input name="phonenumber_txt" id="phonenumberText" cols="45" rows="5" placeholder="Phone Number" required></input>
    </div>

    <input type="submit" id="FormSubmit"></input>

    <img src="images/loading.gif" id="LoadingImage" style="display:none" />
</div>

Could someone show me how an input would be handled using PHP and AJAX/jQuery?

<script type="text/javascript">
$(document).ready(function() {

//##### send add record Ajax request to response.php #########
$("#FormSubmit").click(function (e) {
        e.preventDefault();
        if($("#firstnameText").val()==='')
        {
            alert("Please enter some text!");
            return false;
        }


        $("#FormSubmit").hide(); //hide submit button
        $("#LoadingImage").show(); //show loading image

        var myData = 'firstname_txt='+          $("#firstnameText").val();//build a post data structure
        jQuery.ajax({
        type: "POST", // HTTP method POST or GET
        url: "response.php", //Where to make Ajax calls
        dataType:"text", // Data type, HTML, json etc.
        data:myData, //Form variables
        success:function(response){
            $("#responds").append(response);
            $("#firstnameText").val(''); //empty text field on successful
            $("#FormSubmit").show(); //show submit button
            $("#LoadingImage").hide(); //hide loading image

        },
        error:function (xhr, ajaxOptions, thrownError){
            $("#FormSubmit").show(); //show submit button
            $("#LoadingImage").hide(); //hide loading image
            alert(thrownError);
        }
        });


});

//##### Send delete Ajax request to response.php #########
$("body").on("click", "#responds .del_button", function(e) {
     e.preventDefault();
     var clickedID = this.id.split('-'); //Split ID string (Split works as PHP explode)
     var DbNumberID = clickedID[1]; //and get number from array
     var myData = 'recordToDelete='+ DbNumberID; //build a post data structure

    $('#firstname_'+DbNumberID).addClass( "sel" ); //change background of this element by adding class
    $(this).hide(); //hide currently clicked delete button

        jQuery.ajax({
        type: "POST", // HTTP method POST or GET
        url: "response.php", //Where to make Ajax calls
        dataType:"text", // Data type, HTML, json etc.
        data:myData, //Form variables
        success:function(response){
            //on success, hide  element user wants to delete.
            $('#firstname_'+DbNumberID).fadeOut();
        },
        error:function (xhr, ajaxOptions, thrownError){
            //On error, we alert user
            alert(thrownError);
        }
        });
});

});