Display most recent post in full, excerpts of older posts

This is the basic idea behind what you want. Extend/Customize to your liking.

if ( have_posts() ) :
    while ( have_posts() ) :
        the_post();
        the_title();
        // Incrementing a not instantiated variable results in 1
        // so there's no need to set it to 0 beforehand
        if ( 0 < $is_first_post++ ) the_excerpt();
        else the_content();
    endwhile;
endif;

Or if you want to ommit the compare and the increment operations:

if ( have_posts() ) :
    the_post();
    the_title();
    the_content();
    while ( have_posts() ) :
        the_post();
        the_title();
        the_excerpt();
    endwhile;
endif;

// EDIT to get the one-and-only most recent post in full only:

if (have_posts()) {
    if (2 > get_query_var('paged')) {
        the_post();
        the_title();
        the_content();
    }
    while (have_posts()) {
        the_post();
        the_title();
        the_excerpt();
    }
}