How does one write Right-to-Left in Pages?
For creating an RTL document:


open Pages
Create New Document


in the Chooser, select in the lower left corner "Language" Arabic (Egypt or the region you prefer)

be sure to have the appropriate InputSource (Keyboard) selected
Start typing.


For writing Right-To-Left within an existing document/changing the document to RTL:

File > Advanced > Language &amp; Region –– Select something Arabic

Based on Use bidirectional Arabic and Hebrew in Pages, Numbers, and Keynote

In a document that mixes LTR and RTL scripts:


  Change writing direction:
  On your Mac or iCloud.com: Click Format button , then click Right to left button . 




Caveat: In macOS Pages v7.1 on Sierra and on Pages 8.0 on Mojave this mixing (often?) just doesn't work at all – initially – in a default install with English as the main system language: as the button apparently intended to be used is missing altogether.
On the current iCloud.com version it appears on the right to "Alignment" (as it should in macOS Pages):



That means there is a long running bug in Pages or a common trigger/setup problem that OP and I share. Under these circumstances only typing by hand produces the desired correct RTL orientation for RTL languages.

To get this button to display I had to 


open System Preferences > Language and Region
if not already present: add a Right-to-Left language like Arabic or Hebrew to your list of "Preferred Languages" (via plus button below the list)
drag Arabic to the top position as primary language
restart Pages and quit Pages
drag English back to the primary spot


Pages then seems to retain the ability to display the right-to-Left switch button – and use it. An alternative that's also enabled then is in the menubar: Format > Text > Reverse Text Direction.
(kudos to Tom Gewecke whose comment hit the spot on this one)