Use the double-headed arrow icon to the left of the page names in your section to click and drag pages up and down in the information architecture. This will immediately affect the live site without any "publishing" necessary.
Most areas of the website have no official rules about what order the navigation needs to be in, excepting undergraduate academic sites. For these sites we request that the first three links in the section remain Degree Requirements, Course Descriptions, and Faculty so that these are consistently named and located across our programs for prospective students to find this information.
Another navigation order guideline is that any Contact page is typically found at the bottom of that section's navigation list.
Note: If you need to move a page from the current section to another area of your site, please place a request through web support.