Start off by opening the Themes/babylon | classic | custom_theme/index.template.php file, in this example, we will place the button after the Profile button.
So look for:
// Edit Profile... [profile]
if ($context['allow_edit_profile'])
echo '
<a href="', $scripturl, '?action=profile">', ($settings['use_image_buttons'] ? '<img src="' . $settings['images_url'] . '/' . $context['user']['language'] . '/profile.gif" alt="' . $txt[79] . '" style="margin: 2px 0;" border="0" />' : $txt[467]), '</a>', $context['menu_separator'];
and after that, place:
// The Chat Room
echo '
<a href="', $scripturl, '?action=chat">', ($settings['use_image_buttons'] ? '<img src="' . $settings['images_url'] . '/' . $context['user']['language'] . '/chat.gif" alt="Chat" style="margin: 2px 0;" border="0" />' : $txt[467]), '</a>', $context['menu_separator'];
Then save that and upload the files to your forum, overwriting the existing file.
If you are showing the buttons as images instead of text you will also need to create an image button with "Chat" written on it, save it as chat.gif and upload it to your theme's images/[language] directory as well. (Where [lauguage] is your language)
If you would like the link to go to an external location, you would want to make this part:
<a href="', $scripturl, '?action=chat">To something similar to this:
<a href="http://www.simplemachines.org?">Notice the removal of the ', $scripturl, ' part.

How do I add buttons to the babylon and classic style themes?
.
Thanks for that valuable information. How then can i link up the newly created button with the appropriate page,
say for example linking the CHAT button to my chat room?