If the articles are in pdf format, using pdf annotator (Annotate, Edit and Comment PDF Files. Open any PDF file, add annotations and save all back to PDF in one single step. Fo…) to mark them up works very well.
When I first asked the question, I was limiting my own thinking to free software or apps, but the other responses reminded me of a program that I can highly recommend as a way to collect in one place notes, drafts, and documents, especially for long or research-based projects: Scrivener (http://www.literatureandlatte.com/scrivener.php).
You can get a 30-day free trial (30 days of actual use rather than 30 consecutive days, which is nice) and also a slight educational discount for students and teachers.
If the student has an iPad, Notability is one of the highest rated note taking apps. It has the most features and allows backups to Box and Dropbox, and allows you to save notes as PDFs to read anywhere. Unfortunately, it's not available for Android devices. Another alternative for any platform is Evernote. A number of users swear by it for functionality. I used it for a bit and it's very much an all-or-nothing solution. It works great if you use it for everything, but wasn't very useful for me across several apps.
Hope that helps.
One of my EN132 students asked for ideas for how to take and manage notes electronically (as an alternative to paper index cards), specifically for research papers and keeping track of database articles. I told him I'd put together a list of programs, apps, and ideas. One of his classmates already suggested Microsoft OneNote. Any other suggestions that work for you?