Wordpress - How to display last 3 posts (recent posts) in a static page?

I usually use this approach:

wrong approach

<?php query_posts( array(
   'category_name' => 'news',
   'posts_per_page' => 3,
)); ?>

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

   <?php the_excerpt(); ?>
   <?php endwhile; ?>

<?php else : ?>

   <p><?php __('No News'); ?></p>

<?php endif; ?>

With the help of @swissspidy the correct way is this one:

<?php 
   // the query
   $the_query = new WP_Query( array(
     'category_name' => 'news',
      'posts_per_page' => 3,
   )); 
?>

<?php if ( $the_query->have_posts() ) : ?>
  <?php while ( $the_query->have_posts() ) : $the_query->the_post(); ?>

    <?php the_title(); ?>
    <?php the_excerpt(); ?>

  <?php endwhile; ?>
  <?php wp_reset_postdata(); ?>

<?php else : ?>
  <p><?php __('No News'); ?></p>
<?php endif; ?>

See @codex for more info.

It kind of depends on what you're going for. If you want to do a "page of posts" -- other words, create a new page template file -- you can create a secondary loop on that page.

The codex has an example of this and here's another, very stripped down example.

<?php
/*
Template Name: Page of Posts
*/
get_header(); 
?>

<?php while( have_posts() ): the_post(); /* start main loop */ ?>

    <h1><?php the_title(); ?></h1>

    <?php
        /* Start Secondary Loop */
        $other_posts = new WP_Query( /*maybe some args here? */ );
        while( $others_posts->have_posts() ): $other_posts->the_post(); 
    ?>
        You can do anything you would in the main loop here and it will
        apply to the secondary loop's posts
    <?php 
        endwhile; /* end secondary loop */ 
        wp_reset_postdata(); /* Restore the original queried page to the $post variable */
    ?>

<?php endwhile; /* End the main loop */ ?>

If you're looking for something that you can drop into any page, the best solution would be a shortcode. You would need to create a shortcode that fetches several posts and returns them in a list (or whatever you want). An example:

<?php
add_action( 'init', 'wpse36453_register_shortcode' );
/**
 * Registers the shortcode with add_shortcode so WP knows about it.
 */
function wpse36453_register_shortcode()
{
    add_shortcode( 'wpse36453_posts', 'wpse36453_shortcode_cb' );
}

/**
 * The call back function for the shortcode. Returns our list of posts.
 */
function wpse36453_shortcode_cb( $args )
{
    // get the posts
    $posts = get_posts(
        array(
            'numberposts'   => 3
        )
    );

    // No posts? run away!
    if( empty( $posts ) ) return '';

    /**
     * Loop through each post, getting what we need and appending it to 
     * the variable we'll send out
     */ 
    $out = '<ul>';
    foreach( $posts as $post )
    {
        $out .= sprintf( 
            '<li><a href="%s" title="%s">%s</a></li>',
            get_permalink( $post ),
            esc_attr( $post->post_title ),
            esc_html( $post->post_title )
        );
    }
    $out .= '</ul>';
    return $out;
}

There's a guide for this precise case at the wordpress codex. See it here: I paste the code here because it's quite short, for more information go to the wordpress.org site.

<?php
$args = array( 'numberposts' => 10, 'order'=> 'ASC', 'orderby' => 'title' );
$postslist = get_posts( $args );
foreach ($postslist as $post) :  setup_postdata($post); ?> 
    <div>
        <?php the_date(); ?>
        <br />
        <?php the_title(); ?>   
        <?php the_excerpt(); ?>
    </div>
<?php endforeach; ?>