How to show monthly archive posts?

Create a file date.php in your active theme and use below code, you may need to polish this code as per your requirement:

<div id="content" class="post-archive<?php echo $content_class; ?>">
    <?php if ( have_posts() ) : ?>

        <header class="archive-header">
            <h3 class="archive-title">

                <?php if ( is_day() ) : ?>
                    <?php printf( __( 'Daily Archives: %s' ), '<span>' . get_the_date() . '</span>' ); ?>
                <?php elseif ( is_month() ) : ?>
                    <?php printf( __( 'Monthly Archives: %s' ), '<span>' . get_the_date( _x( 'F Y', 'monthly archives date format', 'fairpixels' ) ) . '</span>' ); ?>
                <?php elseif ( is_year() ) : ?>
                    <?php printf( __( 'Yearly Archives: %s' ), '<span>' . get_the_date( _x( 'Y', 'yearly archives date format', 'fairpixels' ) ) . '</span>' ); ?>
                <?php else : ?>
                    <?php _e( 'Blog Archives' ); ?>
                <?php endif; ?>
            </h3>
        </header>

        <div class="archive-postlist">
            <?php $i = 0; ?>                
            <?php while ( have_posts() ) : the_post(); ?>
                <?php                               
                    $post_class ="";
                    if ( $i % 2 == 1 ){
                        $post_class =" col-last";
                    }                   
                ?>  
                <div class="one-half<?php echo $post_class; ?>">
                    <article id="post-<?php the_ID(); ?>" <?php post_class(); ?>>   

                                                    <?php       
                                                             if ( has_post_thumbnail() ) {  ?>

                                                                    <div class="thumb overlay">
                                                                            <a href="https://wordpress.stackexchange.com/questions/151967/<?php the_permalink() ?>"><?php the_post_thumbnail( ); ?></a>
                                                                    </div>  
                                                    <?php } ?>

                                                    <header class="entry-header">
                                                            <h4><a href="https://wordpress.stackexchange.com/questions/151967/<?php the_permalink() ?>"><?php the_title(); ?></a></h4>
                                                            <div class="entry-meta">
                                                                    <span class="date">
                                                                            <?php echo get_the_date(); ?>
                                                                    </span>


                                                            </div>
                                                    </header>

                                                    <div class="entry-excerpt">
                                                            <?php the_excerpt(); ?>
                                                    </div>

                                            </article>
                </div>
                <?php $i++; ?>
            <?php endwhile; ?>
        </div>
        <?php //fp_pagination(); ?>         
    <?php else : ?>

        <article id="post-0" class="post no-results not-found">
            <header class="entry-header">
                <h1 class="entry-title"><?php _e( 'Nothing Found'); ?></h1>
            </header><!-- /entry-header -->

            <div class="entry-content">
                <p><?php _e( 'Apologies, but no results were found for the requested archive. Perhaps searching will help find a related post.', 'fairpixels' ); ?></p>
                <?php get_search_form(); ?>
            </div><!-- /entry-content -->
        </article><!-- /post-0 -->

    <?php endif; ?>
</div><!-- /content -->