Use wordpress’s in-built “featured image” (can be set on post’s editing page in wordpress admin).
On the page displaying the excerpts:

<div id="excerpts">
    <?php
    $args = array( 'numberposts' => 3, 'category'=> '1,3,5' ); }
    // set number of excepts to show
    // and optionally restrict to certain categories
    $posts = get_posts($args);
    foreach($posts as $post) : setup_postdata($post);
    ?>
    <div class="single-excerpt">
        <h3><a href="<?php the_permalink(); ?>"><?php the_title(); ?></a></h3>
        <?php if ( has_post_thumbnail()) the_post_thumbnail('excerpt-thumb'); ?>
        <!-- displays thumbnail if it exists -->
        <p><?php the_excerpt();?></p>
    </div><!-- single-excerpt -->
    <?php endforeach; ?>
</div><!-- excerpts -->

In your theme’s functions.php:

if ( function_exists( 'add_image_size' ) ) add_theme_support( 'post-thumbnails' );
if ( function_exists( 'add_image_size' ) ) { 
    add_image_size( 'excerpt-thumb', 0, 100, false );
    // define excerpt-thumb size here
    // in the example: 100px wide, height adjusts automatically, no cropping
}

function new_excerpt_length($length) {
    return 42;
    // define length of excerpt in number of words
}
add_filter('excerpt_length', 'new_excerpt_length');