How can I download files from streaming sites?

I'm trying to download files from streaming sites like youtube, soundcloud, etc. I'm aware of tools that exist like youtube-dl, but I'd like to learn how it is done myself.

I've tried looking through chrome inspector to try and find out how the sites work, but I get lost. I've tried looking through the source of youtube-dl, but I get lost there as well.

So, I guess my questions are...

• What topics should I brush up on before attempting to write my own tool?
• How do tools like youtube-dl download files from streaming sites?