Xhost
From Xhost man page:
The xhost program is used to add and delete host names or user names to the list allowed to make connections to the X server. In the case of hosts, this provides a rudimentary form of privacy control and security. It is only sufficient for a workstation (single user) environment, although it does limit the worst abuses. Environments which require more sophisticated measures should implement the user-based mechanism or use the hooks in the protocol for passing other authentication data to the server.
See man xhost for the full info.
Installation
Install the xorg-xhost package.
Usage
To provide access to an application running as sudo or su to the graphical server (aka your X session aka your computer screen), open a terminal and type as your normal user (don't su -):
$ xhost +local:
To get things back to normal, with controlled access to the X screen:
$ xhost -
The 'cannot connect to X server :0.0' output
The above command xhost + will get you rid of that output, albeit momentarily; one way of getting permanently rid of this issue, among many, is to add
xhost + >/dev/null
to your ~/.bashrc file. This way, each time you fire up the terminal, the command gets executed. If you do not yet have a .bashrc file in your home directory, it's OK to create one with just this line in it. If you do not add >/dev/null then each time you fire a terminal, you will see a non-disruptive message saying: access control disabled, clients can connect from any host, which is your confirmation that you can now sudo <your soft> without issue.