Самый простой способ – это отправка почты с помощью функции:

bool mail (string $to, string $subject, string $message
                   [, string $additional_headers[, string $additional_parameters ]])

По мнению автора более надежный способ отправки почты средствами PHP – это отправка письма через SMTP с помощью сокетов.

Ниже приведен код класса для отправки писем через SMTP:

class SendMail {
	private $smtp_username = ""; // имя пользователя
	private $smtp_port     = ""; // порт для отправки почты
	private $smtp_host     = ""; // почтовый smtp-сервер
	private $smtp_password = ""; // пароль
	private $smtp_debug    = ""; // true - включен вывод ошибок
	                                      // false - выключен вывод ошибок
	private $smtp_charset  = ""; // кодировка тела письма
	private $smtp_from     = ""; // имя отправителя

	public function send ($mail_to, $subject, $message, $headers='') {

        $mail_body = "Date: ".date("D, d M Y H:i:s") . " UT\r\n";
        $mail_body .= 'Subject: =?'.$this->smtp_charset.'?B?'.base64_encode($subject)."=?=\r\n";

        if ($headers) {
            $mail_body .= $headers."\r\n\r\n";
        } else {
            $mail_body .= "Reply-To: ".$this->smtp_username."\r\n";
            $mail_body .= "MIME-Version: 1.0\r\n";
            $mail_body .= "Content-Type: text/plain; charset=\"".$this->smtp_charset."\"\r\n";
            $mail_body .= "Content-Transfer-Encoding: 8bit\r\n";
            $mail_body .= "From: \"".$this->smtp_from."\" <".$this->smtp_username.">\r\n";
            $mail_body .= "To: $mail_to <$mail_to>\r\n";
            $mail_body .= "X-Priority: 3\r\n\r\n";
        }

        $mail_body .=  $message."\r\n";

        if( !$socket = fsockopen($this->smtp_host, $this->smtp_port, $errno, $errstr, 30) ) {
            if ($this->smtp_debug) echo $errno."<br>".$errstr;
            return false;
        }

        if (!$this->server_parse($socket, "220", __LINE__)) return false;

        fputs($socket, "EHLO " . $this->smtp_host . "\r\n");

        if (!$this->server_parse($socket, "250", __LINE__)) {
            if ($this->smtp_debug) echo 'I can not send HELO!';
            fclose($socket);
            return false;
        }

        fputs($socket, "AUTH LOGIN\r\n");

        if (!$this->server_parse($socket, "334", __LINE__)) {
            if ($this->smtp_debug) echo 'I can not find an answer to request authorization.';
            fclose($socket);
            return false;
        }

        fputs($socket, base64_encode($this->smtp_username) . "\r\n");

        if (!$this->server_parse($socket, "334", __LINE__)) {
            if ($this->smtp_debug) echo 'Login authentication server has not been adopted!';
            fclose($socket);
            return false;
        }

        fputs($socket, base64_encode($this->smtp_password) . "\r\n");

        if (!$this->server_parse($socket, "235", __LINE__)) {
            if ($this->smtp_debug) echo 'Password was not adopted as a server right! Error authorise!';
            fclose($socket);
            return false;
        }

        fputs($socket, "MAIL FROM: <".$this->smtp_username.">\r\n");

        if (!$this->server_parse($socket, "250", __LINE__)) {
            if ($this->smtp_debug) echo 'I can not send a command MAIL FROM: ';
            fclose($socket);
            return false;
        }
        fputs($socket, "RCPT TO: <" . $mail_to . ">\r\n");

        if (!$this->server_parse($socket, "250", __LINE__)) {
            if ($this->smtp_debug) echo 'I can not send a command RCPT TO: ';
            fclose($socket);
            return false;
        }

        fputs($socket, "DATA\r\n");

        if (!$this->server_parse($socket, "354", __LINE__)) {
            if ($this->smtp_debug) echo 'I can not send a command DATA';
            fclose($socket);
            return false;
        }

        fputs($socket, $mail_body."\r\n.\r\n");

        if (!$this->server_parse($socket, "250", __LINE__)) {
            if ($this->smtp_debug) echo 'No body was able to send letters. Letter was not sent!';
            fclose($socket);
            return false;
        }

        fputs($socket, "QUIT\r\n");
        fclose($socket);

        return true;
	}

	private function server_parse($socket, $response, $line = __LINE__) {
        global $config;
    	while (substr($server_response, 3, 1) != ' ') {
	        if (!($server_response = fgets($socket, 256))) {
	               if ($this->smtp_debug) echo "Problems sending mail! $response$line";
                   return false;
                }
    	}

	    if (!(substr($server_response, 0, 3) == $response)) {
           if ($this->smtp_debug) echo "Problems sending mail!$response$line";
           return false;
        }

    	return true;
	}

}