Don't leave preparation just to the IT department. There's a lot everyone on the team can do to stay in the loop.
Find out quickly what modules are on your site and compare the list to Drupal security advisories
Not technical? Consider Drupal X-Ray. It will give you a complete list of candidates for update.
Basic technical skills with direct access to a backup of the site? Take a look at 2 standard locations in the file structure:
Drupal 7: docroot/sites/all/modules and docroot/profiles/[each possible applicable profile]/[likely a modules subdirectory]
Drupal 8: docroot/modules and docroot/profiles/[likely a modules subdirectory]