How to remove the footer links from Wordpress

Under Appearance click Editor
Click Footer (footer.php) (on the right); scroll to the bottom of the editable part -- should look something like this:

<!-- begin footer -->
<div style="clear:both;"></div>
</div>
</div>
<div id="footerbg">
 <div id="footer">

  <!--Replace the # below with the destination url.-->

  <div class="footer1">
   <ul id="footerwidgeted-1">
    <?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Footer Left') ) : ?>
    <li id="link-list-1">
     <h2>Footer Left Widget</h2>
     <ul>
      <li><a href="#">Link #1</a></li>
      <li><a href="#">Link #2</a></li>
      <li><a href="#">Link #3</a></li>
      <li><a href="#">Link #4</a></li>
      <li><a href="#">Link #5</a></li>
     </ul>
    </li>
    <?php endif; ?> 
   </ul> 
  </div> 
  
  <!--Replace the # below with the destination url.-->
  
  <div class="footer2">
   <ul id="footerwidgeted-2">
    <?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Footer Middle') ) : ?>
    <li id="link-list-2">
     <h2>Footer Middle Widget</h2>
     <ul>
      <li><a href="#">Link #1</a></li>
      <li><a href="#">Link #2</a></li>
      <li><a href="#">Link #3</a></li>
      <li><a href="#">Link #4</a></li>
      <li><a href="#">Link #5</a></li>
     </ul>
    </li>
    <?php endif; ?> 
   </ul> 
  </div>
  
  <!--Replace the # below with the destination url.-->
  
  <div class="footer3">
   <ul id="footerwidgeted-3">
    <?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Footer Right') ) : ?>
    <li id="link-list-3">
     <h2>Footer Right Widget</h2>
     <ul>
      <li><a href="#">Link #1</a></li>
      <li><a href="#">Link #2</a></li>
      <li><a href="#">Link #3</a></li>
      <li><a href="#">Link #4</a></li>
      <li><a href="#">Link #5</a></li>
     </ul>
    </li>
    <?php endif; ?> 
   </ul> 
  </div>
  
  <!--Replace the # below with the destination url.-->
  
  <div class="footer5">
   <p><a href="http://www.studiopress.com/themes/streamline"><img src="<?php bloginfo('tem...'); ?>" /></a></p>
   <p>Copyright &copy; 2009 &middot; All Rights Reserved</p>
   <p><a href="http://wordpress.com">Get a Blog</a> &middot; <a href="http://wordpress.org">WordPress..</a></p>
   <p><a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
      <a href="#"><img style="float:left;margin-top:10px;" src="<?php bloginfo('tem...'); ?>" /></a>
  </div>
  
 </div>
 
</div>
<?php do_action('wp_footer'); ?>
</body>
</html>
  

This part:

<?php if ( !function_exists('dynamic_sidebar') || !dynamic_sidebar('Footer Left') ) : ?>
  

... is a script, written in PHP, telling WordPress,

These are the conditions under which the following links should appear on the web page.

I highly advise that you leave that part alone inasmuch as, perhaps most significantly, any alterations to your PHP script(s) can potentially break your entire site immediately and/or permanently. Not to mention the fact that you may later want to have something there (whether it's the links or something else entirely).

This part:

<ul>
    <li><a href="#">Link #1</a></li>
    <li><a href="#">Link #2</a></li>
    <li><a href="#">Link #3</a></li>
    <li><a href="#">Link #4</a></li>
    <li><a href="#">Link #5</a></li>
</ul>
  

... is the part you want to get rid of to make the links go away. After deleting these lines, be sure to save it by clicking Update File. Once you have saved it, if you go view the site again (and you may need to "refresh" the page once you're viewing it) the footer links that were once there should now be gone.