Ok, trying to expand my knowledge of SQL JOIN

Here is my DB
id parent_id type
1 0 Arts & Entertainment
2 1 Arcades & Amusements
3 1 Concerts
4 1 Carnivals
14 1 Fairs & Festivals
16 0 Automotive
17 16 Accessories
18 16 Dealers & Brokers
19 16 Auto Repair
20 1 Children's & Family Entertainment

I would like to be able to output a list in order like this

Arts & Entertainment
- Arcades & Amusements
- Concerts
- Carnivals
- Children's & Family Entertainment
- Fairs & Festivals
Automotive
- Accessories
- Dealers & Brokers
- Auto Repair

This easy solution for me would be to do something like this

$sql = "SELECT * FROM `advertiser_types` WHERE `parent_id` = 0 ORDER BY `type`";
$result = mysql_query($sql);
while($row = mysql_fetch_array($result)){
print $row['type'].'<br />';
$sql1 = "SELECT * FROM `advertiser_types` WHERE `parent_id` = ".$row['id']." ORDER BY `type`";
$result1 = mysql_query($sql1);
while($row1 = mysql_fetch_array($result1)){
print '- '.$row1['type'].'<br />';
}
}

But Ive been trying to wrap my head around self Joins, the closest thing ive got it this

$sql = "
SELECT parent.type AS 'p_type', child.type AS 'c_type', child.id AS 'c_id'
FROM advertiser_types AS child LEFT OUTER JOIN advertiser_types AS parent
ON child.parent_id = parent.id
";

$result = mysql_query($sql);
while($row = mysql_fetch_array($result)){
if($row['p_type']){
echo $row['p_type'].' - ';
}
echo $row['c_type'].'('.$row['c_id'].')<br />';
}

But I dont completely understand why it works, and also Im not sure how I would get it to sort the alphabetically