How to use Drush in remote server?
It is possible to use Drush with a Drupal site that is running on a remote server that does not have Drush installed.  This is possible because the Drush commands drush rsync and drush sql-sync work by composing ssh commands; if you set up your site alias configuration carefully, then you can copy your site to a local machine to operate on it.

In order for sql-sync to work without Drush on the remote system, you must define the 'databases' and '%dump-dir' variables in your site alias.  Otherwise, Drush will try to use Drush on the remote system to look up these values.  See example.aliases.drushrc.php for more information.

Note that it is really useful to be able to at least run drush updatedb on the remote server, so that you can update your database after you rsync new code over. Of course you can do this through the GUI too, but Drush is faster.  The Resources page on drush.org lists some hosting providers that are Drush-friendly.