We’ve explained before how to use Apple’s Preview to combine multiple PDFs into one document. Turns out you can do the opposite, too – extract single pages from a longer PDF – and the principle is much the same.
First, make sure that the sidebar is showing (press Cmd-Shift-D if it isn’t) and that it’s displaying thumbnails of the pages in the document (if not, press Cmd-Option-2). In the sidebar, click on the thumbnail of the page you want to extract, and then drag it to your desktop.
Preview will now create a new file with just that page, giving it the same name as the original file but with (dragged) as a suffix.
If you Cmd-click to select multiple (even non-contiguous) pages from the sidebar and drag them all to the desktop, you’ll create a single new PDF containing all of them.