there are some plugins that reveal the ID’s on the admin side like
WP Show IDs
and by code like this:
//as dropdown
$categories= get_categories(array('hide_empty' => 0,'taxonomy' => 'category'));
echo '<select>';
foreach ($categories as $category) {
$option = '<option value="'.$category->category_id.'">';
$option .= $category->cat_name;
$option .= '</option>';
echo $option;
}
echo '</select>';
//or just print the categories names by ids like this
$categories= get_categories(array('hide_empty' => 0,'taxonomy' => 'category'));
foreach ($categories as $category) {
echo $category->category_id;
echo $category->cat_name;
}