How do I update CiviCRM following a security update?
First of all, I should say that this is a job for someone who is reasonably technically minded and comfortable with using the command line.  If this doesn't sound like you, then I would suggest that you look for help with this - perhaps from the person that installed CiviCRM in the first place.

You can find detailed instructions in the Administrator Guide.  There are different versions depending on which CMS you use:


Upgrading CiviCRM for Drupal 7
Upgrading CiviCRM for WordPress
Upgrading CiviCRM for Joomla


See also my question on upgrading with drush (Drupal only):

Is it easy to upgrade CiviCRM using drush?

I would strongly recommend that you take a full backup before you do this.  You should also know how to restore from a backup in case anything goes wrong (which does happen unfortunately and can leave your site completely broken).

I would also recommend that you test the update on a development server before you attempt to update the live website. 

If none of this makes any sense to you I think you should probably look for help from someone who has this technical knowledge - e.g. a CiviCRM partner.  Unfortunately, upgrading CiviCRM is not a simple one-click operation like upgrading WordPress.