Add the below snippet to output a list of categories to template, update the terms for custom taxonomies.
$terms = get_terms("category");
$count = count($terms);
if ( $count > 0 ){
echo "<ul>";
foreach ( $terms as $term ) {
echo "<li><a href=". get_home_url() . '/category/' . $term->slug .">" . $term->name . "<a/></li>";
}
echo "</ul>";
}