What is a terminal?
 

And how do I access it in a Suse10.1 with Gnome Ui?

And what do i type in the login screen of Suse Linux 10.1 to pop up the root user?

is it the hostname/password?

1) Look in the programs menu - Different distros put the terminal in different sub-menus, but it is normally under accessories or Utilities.

2) To login as root, enter the command "su" at the prompt (no quotes). It will prompt you for your root user's password.

I hope this helps
--Ian

You can start a session as root, but it is discouraged. - For good reasons.
Use su, or better "sudo" followed by what you want to do as root.

Some brief history.
A video terminal aka console is typically a monitor/keyboard device that connected to a mainframe computer via RS-232 (serial port). What we refer as the terminal in linux is really a terminal emulator. xterm being one of the most used. The typical emulation mode is VT-100 which was a video terminal made by DEC.

A terminal is basically a way to communicate with servers. Terminals or thin clients back in the days had no hard drives. All they could do was send and display recieved information. Xterm is a Terminal Emulator that act's like a terminal. Xterm allows you to send commands to the Linux Kernel from inside of a Window Manager.