Method

An existing page can be cloned by navigating to the Page Admin section, choosing the page to clone, and then clicking the Clone button at the bottom of the screen. 

Outcome

If you clone an existing page you get a new page with links to the same modules as the page you cloned from.

eg
Page A displays modules 1, 2, and 3.
If I clone Page A then I get Page B.
Page B displays modules 1, 2, and 3.

Breaking the link between Modules on the original and cloned pages.

If you decide later that you want to display different content on Page B you will need to remove the modules that you don't want from Page B using the following procedure:
1) Browse to Page B,
2) Click on Site Admin in the User Preferences box,
3) Click on the Modules tab
4) Select the Module that you want to remove from the Edit Module dropdown box
5) Click the Delete button.
The system will break the link between Page B and the module but will not delete the module from the database and will leave the link between Page A and the module so that it still displays on Page A.

Remember also that you can clone modules in a similar process to cloning pages.

If you like, you can clone modules on the new page and delete any references to the original modules.

This will give you a complete copy of the original page with no links between the two.