SQL injections in ADOdb and general website security

I have done pretty much reading and still don't understand 100% how some of the SQL injections happen!

I'd like to see, from those who know, concrete examples of SQL injection based on my example, so it could be replicated, tested and fixed. I have tried to SQL inject my code and couldn't, so I'd like someone to prove me otherwise!

1.Am I right that SQL injection can happen ONLY with POST or GET methods, meaning that on the website it should be the post form, e.g. 'signup or search' or query like 'search.php?tags=love'?

Saying that is this possible to inject the following code that has POST method?

$name     = trim($_POST['username']);
$mail     = trim($_POST['email']);
$password = trim($_POST['password ']);

   if ($errors == "false") {
    $sql = 
        "INSERT INTO 
           clients 
         SET 
           name='" . mysql_real_escape_string($name) . "',
           mail='" . mysql_real_escape_string($mail) . "', 
           password='" . mysql_real_escape_string(sha1($password)) . "'";
           $connection->execute($sql);
        
    }

2.The other one has GET method: rate.php?like&videoID=250&userID=30

$sql = 
    "SELECT 
        videoID 
     FROM 
        likes 
     WHERE 
        videoID = '" .mysql_real_escape_string($videoID). "' AND UID = '" .mysql_real_escape_string($userID). "' LIMIT 1";
        $connection->execute($sql);

Please help those that feel free with the subject but use the concrete examples.

Thanks in advance,
Ilia