Currently a single Google Document can only be either Landscape or Portrait not both. Changing page orientation is done by selecting File and then Page setup…
It is currently recommended to separate the Landscape and Portrait pages into different documents.
A good place to get more information that might help is at Google Products Forums.
Note: An additional option might be to have three files in Google Docs. The Portrait, The Landscape, and Microsoft Word Doc which integrates the two layouts into the correct sequence (this document would be Read Only when viewed in Google Docs).
A Microsoft Word document may allow multiple orientations of the Page Layout, but if it is converted to a Google Document the Page Layout for each page will revert to the first Orientation found in the document.
Also, creating multiple Orientations in Word isn’t as straight forward as one might want either.
For those wanting to do this in Word:
Use portrait and landscape orientation in the same document
Select the pages or paragraphs that you want to change to portrait
or landscape orientation.
NOTE If you select some but not all of
the text on a page to change to portrait or landscape orientation,
Word places the selected text on its own page, and the surrounding
text on separate pages.
On the Page Layout tab, in the Page Setup group, click Margins.
Click Custom Margins. (This is the important part)
On the Margins tab, click Portrait or Landscape.
In the Apply to list, click Selected text..
NOTE Microsoft Word automatically inserts section breaks before and after the text that has the new page orientation. If your document is already divided into sections, you can click in a section (or select multiple sections), and then change the orientation for only the sections that you select.
Updating this as it recently become possible to rotate sections and thus also individual pages in Google Docs.
There are two ways how to change orientation of just a single page in the document:
On page that already exists and which you want to change orientation of select something and go to File -> Page Setup and you should see selection box Apply to. Here select Selected content and choose desired orientation.
This option is very similar to MS Word and allows to change properties of entire section. Create section break starting on new page Insert -> Break -> Section Break (Next Page). Then you can use Format -> Page Orientation or File -> Page Setup and choose section you’ve just created in the Apply to selection box. Choose desired orientation.
First option basically does same thing as second, behind scenes creates a new section and then applies orientation for that section.
If you don’t see options above (particularly Apply to selection box) it might be because you are using corporate Google Workspaces/Apps with conservative new feature rollout policy and this feature wasn’t rolled out to you yet. I tested above successfully on bare GMail account.
On the navigation bar at the top of the page where you have ‘File, Edit, View, Insert etc’ there is a tab called ‘Help’. Type into that tab ‘Page setup’ and it will bring right away the options box which you can manipulate whichever way you like.