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You add or hide menu and block visibility options in System Admin-> Groups. Click on "Modify" for the group concerned, and change access settings in there for blocks and modules. Any changes you make will apply to all members of that group.
For example in the Anon Users group, if you remove a checkmark for access to a module in the "Module access rights" section that link in the main menu will not appear for anon users.
This site has some excellent theme tutorials
http://www.dcdezines.ca/