How can I prevent Supervisor to run at startup?

If it's a service (daemon) install rcconf:

sudo apt-get install rcconf

And then, run it and disable supervisor with it (uncheck its corresponding box, and accept):

sudo rcconf

Whenever you want to run it manually you can use the command:

sudo service supervidor start

sudo service supervidor stop

There's probably a file for it in /etc/init/, probably called supervisord.conf which instructs upstart to start supervisord on boot.

The file will have the start conditions some close to the top, looking somewhat like this (taken from lightdm's init file):

start on ((filesystem
           and runlevel [!06]
           and started dbus
           and plymouth-ready)
          or runlevel PREVLEVEL=S)

Update: As mentioned in the comments, the usual way of disabling an upstart service is creating an override file for that service by issuing the following command:

echo 'manual' | sudo tee /etc/init/supervisord.override

You could also comment those lines using # and supervisord won't start automatically, but changes like that might be overwritten by a future update.

If there is no such file, supervisor might be using old, init-style configs in /etc/init.d/. If that's the case, you can disable it by running

update-rc.d -f supervisord remove