How to display posts by current user/author in a custom page template?

this should work for you:

if ( is_user_logged_in() ):

    global $current_user;
    wp_get_current_user();
    $author_query = array('posts_per_page' => '-1','author' => $current_user->ID);
    $author_posts = new WP_Query($author_query);
    while($author_posts->have_posts()) : $author_posts->the_post();
    ?>
        <a href="https://wordpress.stackexchange.com/questions/23829/<?php the_permalink(); ?>" title="<?php the_title_attribute(); ?>"><?php the_title(); ?></a>       
    <?php           
    endwhile;

else :

    echo "not logged in";

endif;