This article will show you how to take your DHP live.
Instructions
Ensure that Live Edit has been enabled:

Make sure the globals for your new DHP have been either added to the new DHP page or exist under the current department section
Navigate to Modules, then Site Tools, and then Site Map:

Expand the sections you need by clicking on the arrow to the left of the page title:

Find the department that will be getting the DHP:

Find the new DHP Landing Page in the Feature Links section:

Drag the new DHP landing page up to sit right above the current department landing page on the site map:

Move subpages of the current department to be subpages of the new DHP using the site map drag and drop functionality:

To verify that the globals are pulling the correct DHP layout, click to open each global page:

On the opened Global page, navigate to the Layout tab and ensure the Layout is set to Interior and the Theme and Banners match the DHP:

Click Save Layout Changes:

Repeat steps 8 to 10 for each global
Navigate to the DHP landing page:

On the Properties tab, click the Hidden drop-down menu and select the blank space to unhide the page:

Click Save Page Changes:

Open the old department page:

On the Properties tab, check the Hidden option and add "Do Not Delete" to the Menu Text:

Click Save Page Changes:

On the old page, select Add New Version and create a linked page to the new DHP:

Navigate back to your DHP landing page and check that the department global settings are showing up in the global section:

Update layout for mega menus, if applicable
Navigate back to the site map and move the old page to Feature Links:

Note:
Refresh the page to make sure you're moving the correct page and not the new DHP.