Pages in Composer can be reordered by dragging and dropping them in the left navigation bar. Just click to the left of the name of a page and move it to a new position.
Note that you can only reorder pages this way while keeping them under the same “parent” page, but you cannot shift them to a position under a different parent page. You can do that by clicking the More Actions menu to the right of the page's title in the left-hand nav. This will pop open a menu, and one of the options there is "Change Parent." Clicking that menu option lets you choose a new parent for the current page.