storing user input in array

You're not actually going out after the values. You would need to gather them like this:

var title   = document.getElementById("title").value;
var name    = document.getElementById("name").value;
var tickets = document.getElementById("tickets").value;

You could put all of these in one array:

var myArray = [ title, name, tickets ];

Or many arrays:

var titleArr   = [ title ];
var nameArr    = [ name ];
var ticketsArr = [ tickets ];

Or, if the arrays already exist, you can use their .push() method to push new values onto it:

var titleArr = [];

function addTitle ( title ) {
  titleArr.push( title );
  console.log( "Titles: " + titleArr.join(", ") );
}

Your save button doesn't work because you refer to this.form, however you don't have a form on the page. In order for this to work you would need to have <form> tags wrapping your fields:

I've made several corrections, and placed the changes on jsbin: http://jsbin.com/ufanep/2/edit

The new form follows:

<form>
  <h1>Please enter data</h1>
  <input id="title" type="text" />
  <input id="name" type="text" />
  <input id="tickets" type="text" />
  <input type="button" value="Save" onclick="insert()" />
  <input type="button" value="Show data" onclick="show()" />
</form>
<div id="display"></div>

There is still some room for improvement, such as removing the onclick attributes (those bindings should be done via JavaScript, but that's beyond the scope of this question).

I've also made some changes to your JavaScript. I start by creating three empty arrays:

var titles  = [];
var names   = [];
var tickets = [];

Now that we have these, we'll need references to our input fields.

var titleInput  = document.getElementById("title");
var nameInput   = document.getElementById("name");
var ticketInput = document.getElementById("tickets");

I'm also getting a reference to our message display box.

var messageBox  = document.getElementById("display");

The insert() function uses the references to each input field to get their value. It then uses the push() method on the respective arrays to put the current value into the array.

Once it's done, it cals the clearAndShow() function which is responsible for clearing these fields (making them ready for the next round of input), and showing the combined results of the three arrays.

function insert ( ) {
 titles.push( titleInput.value );
 names.push( nameInput.value );
 tickets.push( ticketInput.value );

 clearAndShow();
}

This function, as previously stated, starts by setting the .value property of each input to an empty string. It then clears out the .innerHTML of our message box. Lastly, it calls the join() method on all of our arrays to convert their values into a comma-separated list of values. This resulting string is then passed into the message box.

function clearAndShow () {
  titleInput.value = "";
  nameInput.value = "";
  ticketInput.value = "";

  messageBox.innerHTML = "";

  messageBox.innerHTML += "Titles: " + titles.join(", ") + "<br/>";
  messageBox.innerHTML += "Names: " + names.join(", ") + "<br/>";
  messageBox.innerHTML += "Tickets: " + tickets.join(", ");
}

The final result can be used online at http://jsbin.com/ufanep/2/edit

You have at least these 3 issues:

1. you are not getting the element's value properly
2. The div that you are trying to use to display whether the values have been saved or not has id display yet in your javascript you attempt to get element myDiv which is not even defined in your markup.
3. Never name variables with reserved keywords in javascript. using "string" as a variable name is NOT a good thing to do on most of the languages I can think of. I renamed your string variable to "content" instead. See below.

You can save all three values at once by doing:

var title=new Array();
var names=new Array();//renamed to names -added an S- 
                      //to avoid conflicts with the input named "name"
var tickets=new Array();

function insert(){
    var titleValue = document.getElementById('title').value;
    var actorValue = document.getElementById('name').value;
    var ticketsValue = document.getElementById('tickets').value;
    title[title.length]=titleValue;
    names[names.length]=actorValue;
    tickets[tickets.length]=ticketsValue;
  }

And then change the show function to:

function show() {
  var content="<b>All Elements of the Arrays :</b><br>";
  for(var i = 0; i < title.length; i++) {
     content +=title[i]+"<br>";
  }
  for(var i = 0; i < names.length; i++) {
     content +=names[i]+"<br>";
  }
  for(var i = 0; i < tickets.length; i++) {
     content +=tickets[i]+"<br>";
  }
  document.getElementById('display').innerHTML = content; //note that I changed 
                                                    //to 'display' because that's
                                              //what you have in your markup
}

Here's a jsfiddle for you to play around.