I think you just sign in and click on a big green button "Go to Course" on the right - at least it worked for me with neuralnets course by Hinton, which is really great.
It depends on the course, some courses are kept available and others are shut down after the action is over. I think the choice is left up to the instructors. I started downloading all of the videos when I sign up for a course for this reason actually, because I tend to go through them too slowly to finish with the main group.
For image processing (CNN) https://cs231n.github.io/
For natural language processing (RNN) http://cs224d.stanford.edu/syllabus.html
I also found the following coursera helpful https://www.coursera.org/course/neuralnets https://www.coursera.org/learn/machine-learning