Drupal - How can I install modules using the FTP method?

As kalabro said:

Make sure the folder /sites/default is OWNED by the user that executes the drupal scripts.

On most Ubuntu installations, this is the user Apache user www-data.

chown www-data sites/default

Updating modules using that method works only if the server running Drupal also runs a FTP server; in that case, you need to enter the username and the password to connect to the FTP server. The server is normally "localhost" as both the web server and the FTP server are running from the same IP; if that is not the case, then you should change "localhost" with the name of the server (e.g. ftp.example.com).

If you are running Drupal on your local computer, as when you use it as testing site, then if you don't have a FTP server on your computer, you cannot use that way to update modules; in that case, you just copy the files on your computer, after you download the archives containing the updated versions.

Do not make www-data own /sites/default or any other folder except for /sites//files or /files once the site is live. The "install module" feature within drupal should only be used during site development, when the site is not live. The server should not be able to write to /sites/all or /sites/default or any other folder (except files) as this is a security risk. Again, it may seem convenient to do it that way, but having the server write to any folder except files is a very bad plan. You may be pwned.