When you create a Site, the first page is made for you. There are two ways to create new pages in Google Sites.
Fig.1 Top of a Site page showing buttons and menus
When viewing (not editing) most pages in a site, there are several buttons that allow you to perform maintenance on your Site.
Click the '+Create new page' button to open the dialogue in Fig.2
Fig.2 Create new page dialogue
Page Templates
The default template offered is 'Web page' and this will be what you need most times. The other templates or Page Types have their uses and should be explored at some time.
Naming
Type in a name for the page - make the name short but descriptive, one that makes sense to another human reading it!
Hierarchy
Now choose where in the Site's hierarchy the page will sit. Choose 'Top level' if the page is the start of a major theme on the site. If the page is subordinate to the page that you are linking from then choose to 'Put the page under ...' In the image above this option happens to be 'White Scar Cave - Field Trip' but this will be the name of the page you were on when you clicked the 'Create page' button.
If you want to create the page somewhere else in the hierarchy, click 'Choose a different location' to open a dialogue where you can select another page to be subordinate to. There is more detail on the Create Link page
This process is described in more detail on the Create Link page