Best way to use PHP to encrypt and decrypt passwords?

You should not encrypt passwords, instead you should hash them using an algorithm like bcrypt. Still, here is how you would encrypt/decrypt:

$key = 'password to (en/de)crypt';
$string = ' string to be encrypted '; // note the spaces

To Encrypt:

$iv = mcrypt_create_iv(
    mcrypt_get_iv_size(MCRYPT_RIJNDAEL_256, MCRYPT_MODE_CBC),
    MCRYPT_DEV_URANDOM
);

$encrypted = base64_encode(
    $iv .
    mcrypt_encrypt(
        MCRYPT_RIJNDAEL_256,
        hash('sha256', $key, true),
        $string,
        MCRYPT_MODE_CBC,
        $iv
    )
);

To Decrypt:

$data = base64_decode($encrypted);
$iv = substr($data, 0, mcrypt_get_iv_size(MCRYPT_RIJNDAEL_256, MCRYPT_MODE_CBC));

$decrypted = rtrim(
    mcrypt_decrypt(
        MCRYPT_RIJNDAEL_256,
        hash('sha256', $key, true),
        substr($data, mcrypt_get_iv_size(MCRYPT_RIJNDAEL_256, MCRYPT_MODE_CBC)),
        MCRYPT_MODE_CBC,
        $iv
    ),
    "\0"
);

---

Demo at IDEOne.com:

echo 'Encrypted:' . "\n";
var_dump($encrypted); // "ey7zu5zBqJB0rGtIn5UB1xG03efyCp+KSNR4/GAv14w="

echo "\n";

echo 'Decrypted:' . "\n";
var_dump($decrypted); // " string to be encrypted "

Found this class recently, it works like a dream!
class Encryption {
    var $skey = "yourSecretKey"; // you can change it

    public  function safe_b64encode($string) {
        $data = base64_encode($string);
        $data = str_replace(array('+','/','='),array('-','_',''),$data);
        return $data;
    }

    public function safe_b64decode($string) {
        $data = str_replace(array('-','_'),array('+','/'),$string);
        $mod4 = strlen($data) % 4;
        if ($mod4) {
            $data .= substr('====', $mod4);
        }
        return base64_decode($data);
    }

    public  function encode($value){ 
        if(!$value){return false;}
        $text = $value;
        $iv_size = mcrypt_get_iv_size(MCRYPT_RIJNDAEL_256, MCRYPT_MODE_ECB);
        $iv = mcrypt_create_iv($iv_size, MCRYPT_RAND);
        $crypttext = mcrypt_encrypt(MCRYPT_RIJNDAEL_256, $this->skey, $text, MCRYPT_MODE_ECB, $iv);
        return trim($this->safe_b64encode($crypttext)); 
    }

    public function decode($value){
        if(!$value){return false;}
        $crypttext = $this->safe_b64decode($value); 
        $iv_size = mcrypt_get_iv_size(MCRYPT_RIJNDAEL_256, MCRYPT_MODE_ECB);
        $iv = mcrypt_create_iv($iv_size, MCRYPT_RAND);
        $decrypttext = mcrypt_decrypt(MCRYPT_RIJNDAEL_256, $this->skey, $crypttext, MCRYPT_MODE_ECB, $iv);
        return trim($decrypttext);
    }
}

And to call it:
$str = "My secret String";

$converter = new Encryption;
$encoded = $converter->encode($str );
$decoded = $converter->decode($encoded);    

echo "$encoded<p>$decoded";