How to run an X program as a different user?

[Robert Latest <boblatest@googlemail.com>]

Hello all,

my question is already in the subject line. Also I think that I've got
the basics figured out, it's just that I don't understand the details.

Essentially I want user A to run a specific X app as user B. So I
think I need to write a tiny shell script like this:

#!/bin/sh
xhost +B
sudo -u B /path/to/app arg1 arg2 arg3
xhost -B

I need help with two things though:

One, "xhost +B" doesn't work, contrary to the manpage. "xhost +"
works, granting X access to the entire Net, but who cares. This is
just a home computer.

Two, I can't figure out for the life of me what the entry in
/etc/sudoers must look like to make sudo do what I want.

Thanks,
robert