These were the steps I used to install drush globally using composer in Linux (not in ~/.composer/vendor/bin logged in as root which makes absolutely no sense):

 1. Login as root
 2. Install composer if necessary. See. http://getcomposer.org/doc/00-intro.md#system-requirements.
 3. composer global require drush/drush:6.*
 or
 composer global require drush/drush:dev-master
 4. cd ~/.composer
 5. composer config --global bin-dir /usr/local/bin
 6. composer config --global vendor-dir /usr/local/share
 7. composer install
 8. cp -r vendor/ /usr/local/share/drush/drush/
 9. cd /usr/local/share/drush/drush
 10. composer install

Now any user with /usr/local/bin in their path can run drush. Security precaution: You might want to chown and chmod /usr/local/bin/drush so only authorized users in a certain group can execute drush.

Notes: Lines 5 and 6 create the file ~/.composer/config.json. Line 10 is needed to delete (yes, delete) the /usr/local/share/drush/drush/vendor/drush folder which is unnecessary.