How do I set up pages so that the Book title is on a left page and the chapter title is on a right page?

In a book, how can I put the Book Title on a left page, and the Chapter Title on a right page?

You use page styles to select whether pages are to be left, right or both. Normally page titles would be on the right hand side but that is up to you. You can adjust the Title page directly by choosing FORMAT > TITLE PAGE > EDIT > PAGE > LEFT ONLY. (The default name will be FIRST PAGE). For the Chapter you will need to create a new Chapter Page Style perhaps based on the FIRST PAGE as this has a suitable layout for a chapter title page. You can use the Sidebar for this, F11 > STYLES and FORMATTING > Page Styles > Right click on First Page > NEW > Change Name or Organiser > Page > Only Right.

Styles are very useful, you will find some information on the LibO HELP. I would also recommend the LibO Writer Manual Chapter 4 - Formatting Pages. You can download the chapters or books from the web site Hope this helps …Peter

(Editing: My post crossed the one by @petermau. I did not delete it because of its different approach and its different interpretation of the question.)
You surely will use headers with different settings left/right?
I would use document variables for the titles. Variables can be defined (setting a value) via > ‘Insert’ > ‘More Fields…’ > tab ‘Variables’ > selection ‘Set Variable’ … (You may start with Ctrl+F2 bypassing the menu.)
A variable defined this way can be shown in any place (use same dialogue tab!). It then can be edited in one place with effect on each occurrence.
If you only choose different headers, you may directly type the titles into the header variants for left/right directly.