How would one go about self-studying neuroscience to the level of say, a second year grad student not yet specializing in anything? That is to say, familiar with the basic concepts and able to make sense of current research given enough time.
The Neuroscience book by Mark Bear gives a nice introductory overview of the biology behind a lot of neural processes: https://www.amazon.com/Neuroscience-Exploring-Mark-F-Bear/dp...
If you're interested in computational neural models, I would highly recommend Wolfgram Gerstner's recent book (available for free online): http://neuronaldynamics.epfl.ch
The book by Dayan and Abbot on theoretical neuroscience is quite nice too: https://mitpress.mit.edu/books/theoretical-neuroscience
After this, you'll probably want to read new review papers, since it's a field that's moving quite fast now. (Especially with new measurement techniques in the past few years)
Start with "Fundamentals of Neuroscience" by Harvard, free multimedia course that requires only a high school level education:
then go to
"Medical Neuroscience" on Coursera (the professor is a great teacher):
https://www.coursera.org/learn/medical-neuroscience
Especially the 2nd course is pretty big, on of the largest online courses there is in terms of videos to watch and things to learn. But while it is a lot it is much easier than the quantum mechanics course(s) half the size on edX. You don't have to think much, just listen and learn.
Aft hat you have a very solid foundation, now check out more such courses on the same platform.