To add the new user, go into System -> Administration -> Users and Groups.
You can add a new account from here which you should definitely give limited permissions. I would set the account type to 'Desktop User'.
You can then click on 'Advanced Settings', click the 'User Privileges' tab and untick the following:
- 'Connect to the internet using a modem'
- 'Connect to wireless and ethernet networks'
This should disable the internet.
I don't think there is an easy way to not show the whole 'System' menu but you can disable menu items using
alacarte by right clicking on the menu bar and clicking edit menus. As long as the new user account doesn't have administration privileges, they can't do any harm to the system through these menus anyway. She won't be able to do anything with the System -> Administration programs for instance. The worst thing she can do is completely mess up her theme and delete all her personal files but this will not affect the system as a whole.
Alternatively, if there is only a small number of programs you want her able to access, you could delete the menu applet from the top panel and add shortcuts to the desktop of the programs you want her to access.
See this question for other parental control options.
You may be interested in a program called GNOME Nanny although it is still under development and there are no stable releases.