How to quickly update/reinstall using Drush 4.x
It's best practice to always backup your database first when updating modules (especially when working with -dev versions). A useful module is Backup and Migrate, when installed it also provides a Drush command to backup the database (drush bb). (But avoid GZ compression at the moment, bug introduced with version 2.3). Since you currently have a fatal error, you'll probably have to make a backup of your database via your database management tool in Ubuntu, or use something like phpMyAdmin. You should also note which modules you will update and what the currently installed versions are. If you do all upgrading via Drush, it creates a backup of all modules it updates (so you don't have to keep track manually), and if something goes really wrong you can go back to the previously working code and if necessary put your backed-up database in place.

It looks like the current version of your Flag module is throwing the fatal error which is preventing you from updating / accessing the site. I assume this is still an old version (cf. e.g. this report), and it's likely that if you put the latest recommended relase of Flag in place the error goes away (remove the current flag module folder and replace with the 7.x-2.0-beta6 version). (If this doesn't solve the Fatal error, you should provide some more details on what versions of Flag and Rules you were using previously, and what version they are at now).

Once you get the site back working, it's a matter of doing the regular Drush commands from your Drupal directory. For example:

# If you have many sites you can check to make sure you're working on the right site
drush status

# update all modules but not Drupal core
drush up --no-core

# make sure update.php is run (in my experience sometimes some updates aren't run)
drush updatedb


Now check that your site is still working properly and then update Drupal core.

drush up drupal


And check your site again. The status report will show you if all modules and themes are up to date and if there are any database upgrades that still have to be executed.

For more info on Drush also check out drush.org.