In DokuWiki, pages are created as in every other wiki. Simply create a link from an existing page to a non-existing page, follow this link, and click on Create this page (bottom left, directly above the footer). This is the most common and recommended way.
There's also a screencast available explaining it in detail.
Of course you can also open a non-existing page by manually manipulating the URL in your Browser. For example, to create a new page newpage in the namespace playground, one has to replace documentation/pages with playground/newpage in the URL, load the new site and click on Create this page.
NOTE: Make sure you properly link your newly created page from other pages. Otherwise no one may find your page. (Though these pages may still be found by the Sitemap feature or through the search engine.)
Page names are converted to lowercase automatically. Allowed characters are letters, digits and, within names 1), the “special characters” ., - and _. All other special characters (i.e. other than letters and digits – whitespace, plus, slash, percent, etc.) are converted to underscores. Colons (:) are used to identify namespaces
Editing a page is done by clicking the Edit this page button (bottom left, directly above the footer) unless the page is created.
The creation or editing of a page leads you to an edit window that enables you to enter text using the syntax of Dokuwiki. Editing a page consists in putting your text inside the edit area, and adding some markup to enhance its layout.
In order to help you in the editing process, a preview feature enables you to look at the formatted page before saving it.
Once your page does match your criteria, you hit the save button in order to save it. The page is then rendered into HTML, which is the standard output.
If you save an empty page, then DokuWiki will delete the page, and the associated pagename. (Note that the attic (old revisions) remains.)