Post the output from the command as above and 'id'. You have to be just member of the dialout group and access should be rw - exactly as above. Or try 'sudo chmod a+rw /dev/ttyUSB0'.
A quick way to get all of this working if you can't get 'dialout' permissions to change, is to simply run the app as a super user.
$ sudo arduino
then enter your root password on prompt
Running as super user will give you access to both dialout and tty port permissions, without having to run chown or chmod.
The downside is that it saves your arduino program files in your root accounts home directory, so make sure to specify your file save paths when you back up your programs.
I couldn't get my OS to give me permissions for dialout, this fix worked for me.