This is a relatively simple task, and you only need to attach an appropriately coded page template to your chosen post’s page.

When the page first loads, the main query holds data on the page, such as the title, content and so forth, we can shortcut to that by calling the_post which will then allow us to simply call the template tags to produce the title(etc) for the page. Following that we can then call query_posts and refill the main query object with a selection of posts.

This is very similar to the examples given on the codex, here.
http://codex.wordpress.org/Pages#A_Page_of_Posts

The main difference here, is that rather than creating a second query object, i’m just going to re-use the main one(why not, it makes sense in this context, imho).

Adjust the code(Query parameters/HTML/Classes/IDs) as appropriate.

<?php
/**
 * Template Name: Page of Posts
 *
 * Selectable from a dropdown menu on the edit page screen.
 */
get_header(); 
?>

<div id="container">
    <div id="content">

        <?php the_post(); // Setup post data so it's possible to call the regular loop template tags ?>
        <h2><?php the_title(); ?><h2>
        <div <?php post_class(); ?>><?php the_content(); ?></div>

        <?php 
        $args = array( 
            'paged' => (int) get_query_var('paged'), 
            'post_type' => 'post', 
            'order' => 'desc', 
            'posts_per_page' => 3, 
            'caller_get_posts' => 1 
        );
        // Now re-define the main query
        query_posts( $args ); 
        ?>

        <?php if( have_posts() ) : ?>

            <?php while( have_posts() ) : the_post(); ?>

                <h2><?php the_title(); ?></h2>
                <div <?php post_class(); ?>><?php the_content(); ?></div>

            <?php endwhile; ?>

        <?php endif; ?>

    </div>
</div>

<?php //get_sidebar(); ?>
<?php get_footer(); ?>

Hope that helps..

Updated response follows

The template that deals with a post’s page will differ if you use the page_for_posts setting, don’t try to use and a page template, use one or the other, since both will not work together.

When you want to show the post list/index on a page, and let your native theme files deal with rendering, set the page_for_posts setting(admin > settings > reading).

When you need to control how a page of posts renders, and do something custom with it, rather than fiddle around in the theme files trying to work out which file is dealing with the output, then adding conditional logic, instead create a page(or choose an existing one) and attach a page template to it. Only by not setting the page_for_posts setting do you allow this page to render using the attached template.

Ignore my front page setting, obviously you may have a more appropriate page set for that, simply notice how i’ve not set the posts page setting. If you set yours as done in the screenshot, the template provided will work correctly, and the posts page will behave just as it would when setting the posts page setting(except it will obviously do some custom stuff to).

Summary
– When you set the page_for_posts setting you fore-go any ability to attach a template to that page, unset it and the template will work as expected.

Edit: Rarst actually pointed out this behaviour to, in your other question…
Template file for static posts page does not get loaded