Hi,
I'm asking because my only experience of what these types of armies looked/fought like is from the total war series, so I'd like to rectify that. I want to start out with an overview since I know nothing on the matter (just like Jon Snow).
Though I asked for an overview, the following points are of particular interest to me:
How would they be composed of (including size, regional variations, etc.)?
How would they be organized?
How were they led/how did the chain of command work?
Any conceptions of armies that I need to get rid of to understand a medieval army?
Also, if you think there are good book recommendations out there, please recommend them.
Not knowing what your conceptions are, it is not possible for anybody to tell you which ones you need to get rid of :D.
However, my first recommendation on the topic is Fighting Techniques of the Medieval World: Equipment, Combat Skills and Tactics by Bennett, Bradbury, et al.
The "Fighting Techniques" series of books are quite good introductions to learners, and they are a very nice read.
Enjoy!