The following tutorial, will describe how to dynamically update your page with view results. It will be based on the Drupal & Ajax - Basic Tutorial, which breaks down the steps of implementing basic Ajax with Drupal. So if you still haven't read it, now will be a good time to do so.
I will also use the code from that tutorial to extend the implementation.

What I'm going to add in this tutorial is:

1. Load an existing view.
2. Setup view parameters for execution.
3. Execute the view.
4. Load the themed view to the JSON object and return it.

As you will see, there's no much difference between returning a simple static list of categories as I've done in the basic tutorial, and returning a view result. At the end of the day, both are html streams that are loaded to a JSON object which is returned to the client.
NOTE: If you already have a view that you want to use, you can skip steps 1-3, and use your own view (Skip to step 4).

Step 1 - Create "Product" content type
Let's define a new content type. This content type will be used to create content that we will use in this tutorial.
We will call our new content type "Simple Product". Define the following fields for the new content type we just created as follows:

• Description
• Price
• Category

Only for the simplicity of this example, go ahead and define all fields as simple text fields.

Step 2 - Create content
It is now time to create "Simple Product" content items, so create a list of products(at least 6 products).
In the "Category" field value, for each content item, set one of the following values "books" or "movies" (3 products per category). This value will help us later to return a list of products based on that category.

Step 3 - Create the view
The next task you will need to complete is to create a view. It is out of the scope of this tutorial to explain how to do that, so if you are not familiar with the Views module, I urge you to read more about it before you continue.
So, with the Views modules, create a new view as follows:

• Name the new view "products_by_category".
• Define the fields you want this view to return
• Define a view argument (type should be Content:Category).
• Test your view to verify it returns the products you expect per category argument

Step 4 - Execute the view
If you remember, the original .module code, created a static html list, which was loaded into a JSON object and was returned as the function output as follows:

function dynamic_products_get_by_category_id($cat_id){
  $items = '';
  switch($cat_id){
    case 12: 
     $items = '<ul><li>Product 1</li><li>Product 2</li></ul>';
     break;
    case 20:
     $items = '<ul><li>Product 3</li><li>Product 4</li></ul>';
     break;  
  }
// create a JSON object. The object will contain a property named “products” that will be set with the $items variable. 
  return drupal_json(array('products'=>$items));
  exit;
}

The following code, calls the view we want to load, and returns its result

function dynamic_products_get_by_category_id($category){

  $viewName = 'products_by_category'; // The name of the view we are going to load

  $args = array($category);  // Array of arguments we set for the view. Only one argument in our example. your actual view may require additional arguments which you may need to set

  $displayId = 'page'; // The display id of for the view. 

  // Call the views_embed_view function to returned themed view output
  $res = views_embed_view($viewName, $displayId, $args);

// create a JSON object. The object will contain a property named “products” that will be set with the themed result of the executed view. 
  return drupal_json(array('products'=>$res));

  exit;
}

Few notes about the code:
This line, sets the arguments that should be passed to the view. In our case, the view accepts a single argument which is the category.

  $args = array($category); 

  $res = views_embed_view($viewName, $displayId, $args);

  return drupal_json(array('products'=>$res));

The views_embed_view function, which you can read more about it here, is called to return a themed result.
The function accepts as input parameters, the view name, the id of the display (i.e. default, page, block, etc.), and an array of view arguments.
The result, is html output containing the result of the view. This view can be themed as you would theme it if it wasn't loaded dynamically.
After we have the view result, we load it into a JSON object which will be returned as a response to the AJAX request.

Step 5 - Update page code
The last chnage we are going to make is to the page's code. The Html in the original tutorial was:

 
<div id=”topDiv”>
<a class="categoryLink" href="/products/get/12">Cat. 1</a>
<a class="categoryLink" href="/products/get/20">Cat. 2</a>
</div>
<div id="divProducts”></div>

We are going to change it to pass the correct category according to what we defined in step 2 ("books" or "movies"):

 
<div id=”topDiv”>
<a class="categoryLink" href="/products/get/books">Books</a>
<a class="categoryLink" href="/products/get/movies">Movies</a>
</div>
<div id="divProducts”></div>

That's it. You should be able to save and test you code.