When you create a new story and click on Publish you will be presented with two options:

  1. Publish on LivePost.
  2. Publish on your site.

Make sure to click on "Publish on your site" to see your story's embed code. This code is very similar to a Youtube video embed code. To embed your story on your blog:
  1. Copy the code.
  2. Go to your blog.
  3. Create a new post.
  4. Paste the code right where you write your post.

You can also find your story's code in your story's settings.

Here's how to embed LivePost on Wordpress.org.