1. check if pear is installed
# pear version
PEAR Version: 1.9.4
PHP Version: 5.3.3
Zend Engine Version: 2.3.0
2. add the drush channel
# pear channel-discover pear.drush.org
Adding Channel "pear.drush.org" succeeded
Discovery of channel "pear.drush.org" succeeded
3. change to the folder where your drupal site is installed
example given:
# cd /public_html/site_xy
4. update to the new drupal version (example drupal 7.24)
# drush pm-update projects drupal-7.24
you are done
Further documentation on drush specific installation issues:
https://drupal.org/node/1791676