PDFs will load by default in the browser window, so you will be able to read them without having to download them. However, if you would like to download them to save them for later, you can do that as well.
To save a PDF, open the Google Chrome menu in the upper left corner of the screen (it looks like three horizontal lines). Choose "Save page as..." to save the PDF. Where you save the file depends on a few things:
Microsoft Office files will open in a program called Quickoffice on the Chromebook. This will allow you to view and edit the file as you would on a regular PC. If you need to save the file, open the "File" menu near the upper right corner of the screen and choose "Save as...". From there, choose one of the options below.