Updates are rather simple.
All you have to do is to enter the members area (using the customer number/password you were given at the time of purchasing a license), then download the latest version for your version tree. 3.8.5 is the latest stable for 3.x and 4.0.4 is to be soon the latest stable in 4.x.
Then, you take the zip package and upload the contents of the upload files, overwriting all of the files on the server. You may like not to upload favicon.ico and config.php.new : these files aren't part of the upgrade
After you've done that, you point your browser to
http://yourdomain.com/forums/install/finalupgrade.php (or wherever your forums are installed) and run the upgrade script. Once that's done, you are finished upgrading to the latest version of vBulletin you downloaded.
Hope this helped you.