There are a number of apps to assist you taking notes. Onenote and Evernote both allow you to capture most anything you wish and access it from any device.The two tools organize notes differently, so choose the one that works best for you. Taking a more simple and minimal approach are Google Keep and Simplenote. These are to Onenote and Evernote as a notepad is to a notebook. You are able to take notes, but perhaps not so long-form. Diigo is primarily a web research tool, allowing you to comment/mark-up and clip webpages and bookmarks. It also will markup PDFs that are opened in a browser. Any markup is saved to a users library. Pen(cil) & paper are always a good option. This option is as portable as you want it to be, requires no power, and is always ready to go. Some would suggest that taking notes by hand may even help a person retain information and perform better academically, Penultimate allows you to do this digitally. Investigate the links below to try each of these tools.
If you are considering taking notes digitally, this list of styli may be helpful.