Can you recommend how to learn this? I don't work with the web or networking, and would like to shore up that part of my knowledge. Are there any good books that gives the high-level overview of it all?
I find that the best way to learn it is to start poking at it. Fire up Wireshark, load google.com, and take a close look at the traffic. You'll see every packet going back and forth, and can try to figure out what each one of them is. Set up a proxy that can MITM the SSL connection, and look at the contents of the packets. Just setting that up will probably tell you a lot about how it all works, and you'll be in a better position to see the plaintexts of all of the handshaking traffic.
The first question has had a semi-famous answer from this post in 2011: https://plus.google.com/+JeanBaptisteQueru/posts/dfydM2Cnepe I'd be interested to know what if any books people recommend as well, though my own strategy is when encountering a black box, and desiring to learn about it, I learn about it using whatever resources I can find to make it transparent (often revealing many internal black boxes...). Occasionally online I'll find someone who made really good visual diagrams that help summarize a thing that I might not have found otherwise in a book, e.g. http://code.google.com/p/corkami/wiki/ELF101 or http://brendangregg.com/linuxperf.html