The TinyMCE module comes packaged with the drupalbreak plugin. This TinyMCE plugin (not the Drupal module) adds two buttons that create a teaser or page break. (The teaser break is a built-in Drupal core feature. The page break requires the paging module.)
The code to create these breaks is:
<!--break-->
<!--pagebreak-->
1. Copy the entire directory tinymce/plugins/drupalbreak into the plugins directory of the TinyMCE actual. (tinymce/tinymce/jscripts/tiny_mce/plugins/)
% cd ~/public_html/drupalbase/
% cp -r modules/tinymce/plugins/drupalbreak/ modules/tinymce/tinymce/jscripts/tiny_mce/plugins/
2. To add the break buttons to your TinyMCE profile, first insert the following lines to modules/tinymce/plugin_reg.php. Place them near the end of the file, just before you see return $plugins.
$plugins['drupalbreak'] = array();
$plugins['drupalbreak']['theme_advanced_buttons3'] = array('drupalbreak', 'drupalpagebreak');
3. Add the buttons to your TinyMCE profiles at admin/settings/tinymce.