The best way to replace a PDF is to delete and then reupload the PDF.
First, upload the new PDF using the Desktop Media Uploader. Click on the link and click the link button in the top menu.
Select the "Media" tab and find the new PDF.
Go to the "Media" section and find the old form. Right click on it in the navigation tree and select "delete."
If there are links to the PDF that are outside of your control (in Self-Service, Joule, etc), upload the new PDF in the place of the old one.
First, make sure the file is named the same as the previous file. E.g. Student Handbook 2014.pdf
Find the document in the "Media" section of Umbraco.
Click the "Choose File" option and pick your new file. Click save.
Browsers cache (save) versions of files sometimes to improve speed. Normally we don't worry about this, but if you are worried, the link should have something added to the end. For instance, http://www.masters.edu/media/384487/ADD-DROP.pdf becomes http://www.masters.edu/media/384487/ADD-DROP.pdf?2014
Anything after the question mark doesn't matter, but don't use punctuation. The actual link is the same, it's just a way for the browser to know to get the newest version.