add an opening <ul>
before the if(.....
and add the closing </ul>
after the endif;
and remove most of the stuff in the middle, as you will never see it again using widgets:
<div id="sidebar">
<ul>
<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar() ) : ?>
<?php wp_register(); ?>
<li><?php wp_loginout(); ?></li>
<?php wp_meta(); ?>
<?php endif; ?>
</ul>
<div class="box" id="share">
<a href="/feed/"><img src="<?php bloginfo('template_url')?>/images/rss.jpg" alt="RSS feed" /></a>
<a href="https://www.facebook.com/CHANGE_THIS"><img src="<?php bloginfo('template_url')?>/images/facebook.jpg" alt="Facebook" /></a>
<a href="https://www.twitter.com/CHANGE_THIS"><img src="<?php bloginfo('template_url')?>/images/twitter.jpg" alt="Twitter" /></a>
</div>
</div><!-- ======= sidebar END ======= -->
to remove the bullet points in the sidebar, add a new line in style.css:
#sidebar ul {list-style-type:none;}
and then start with adjusting the padding and margins in #sidebar ul
and #sidebar ul li
(add these styles)
#sidebar ul {padding:0; margin:0; }
#sidebar ul li {padding:0 10px; margin:0; }
(to get full control, you may also need to style #sidebar ul ul
and #sidebar ul ul li
)