When you wish to logout, simply position the mouse on the gnome icon in the control panel at bottom or top of screen. Then, press the left-most mouse button and select the Quit option from the bottom of the menu, then release the button. The screen should clear, and in a few seconds the original login prompt should return. If your window manager exits but you aren't logged out, try logging out of all open shells by typing exit at their prompts or push Ctrl+Alt+BackSpace key to restart X. If successful, the gdm or xdm login manager you saw at login should reappear.
When you wish to logout from a dial-up session, type either logout, exit, or control-D to disconnect from the workstation, then again to disconnect from the dial-up server.