Currently there is no way to directly annotate PDFs without installing software specifically designed for this task (although many citation managers, like Mendeley, allow you to highlight and write notes on PDFs within your citation library). There are several software options available. Some are free (often with paid premium options) and some are fee based.
Foxit Reader - A multilingual PDF tool that can create, view, edit, digitally sign, and print PDF files. Available for Windows computers and phones, Apple iOS, and Android phones.
Okular - A universal document viewer for Linux, Windows, and Mac.
PDFescape - Online PDF reader, editor, form filler, and form designer. Available online and for Windows desktop.
Mac and iPhone
iAnnotate - Apple app which lets you read, annotate, and share PDFs, Microsoft Office files, images and web pages.
Acrobat Pro - Edit PDFs and turn scans into editable documents. Multi-platform, and available on some campus computers.
PDF Annotator - Allows you to add notes and annotations to any PDF document. You can handwrite your notes if you have a touch screen. (For Windows computers and tablets, with free trial)
PDFpen - Turns scans of text into editable PDFs and Microsoft Word documents. (For Mac, with free trial)