Find the Children of a Page then Echo it as a Bulleted List of Links (menu)

Well you just need to run a foreach loop over your $children but WordPress has a build in function for this already called wp list pages.

For example:

$children = wp_list_pages('title_li=&child_of=".$post->ID."&echo=1');

if ($children)
echo '<ul>' . $children . '</ul>';

There is a full reference and examples here: http://codex.wordpress.org/Function_Reference/wp_list_pages