How are Operating Systems "Made"?
Operating Systems is a huge topic, the best thing I can recommend you if you want to go really in depth on how a operating systems are designed and construced it's a good book:
Operating System Concepts
If you are truly curious I would direct you to Linux from Scratch as a good place to learn the complete ins and outs of an operating system and how all the pieces fit together. If that is more information than you are looking for then this Wikipedia article on operating systems might be a good place to start.
A PC knows to look at a specific sector of the disk for the startup instructions. These instructions will then tell the processor that on given processor interrupts, specific code is to be called. For example, on a periodic tick, call the scheduler code. When I get something from a device, call the device driver code.
Now how does an OS set up everything with the system? Well hardware's have API's also. They are written with the Systems programmer in mind.
I've seen a lot of bare-bones OS's and this is really the absolute core. There are many embedded home-grown OS's that that's all they do and nothing else.
Additional features, such as requiring applications to ask the operating system for memory, or requiring special privileges for certain actions, or even processes and threads themselves are really optional though implemented on most PC architectures.
Well, the answer lives in books: Modern Operating Systems - Andrew S. Tanenbaum is a very good one. The cover illustration below.
The simplest yet complete operating system kernel, suitable for learning or just curiosity, is Minix.
Here you can browse the source code.
(source: cs.vu.nl)