They say to go to the print menu and do it there. But after I've done this, I click 'done' and the size of my page does not appear to change.
Later, I'm going to embed this PDF inside another document and I don't want there to be a lot of white space. Currently the bottom half of my A4 page is empty.
Use the artboard tool to select he art board you want to change. Then double click the artboard tool in the tool panel. Now you can enter a new size and position of the artboard.
You can also click the edit artboard button in the document setup to manually resize the artboard. Or just select it with the artboard tool to resize it manually.
Resizing all artboards at once is not possible. Perhaps a script or plug in. They are not actually pages and unlike a page layout program they can be different sizes in the same document. The designer who needs to control the publications graphic system in a consistent way throughout the publication. Do not even know if it is possible to eventually do.
You can only select one art board at a time. Keep in mind Illustrator is not a layout program but a vector art creation program. So the artboards are not actually pages.