Hardware clock signals implementation in Linux Kernel

What you want to achieve is highly specific to a) the platform you are using and b) the device you want to use. For instance, on x86 there are 3 ways to communicate with a device:

1. Interrupts allow the device to signal the CPU. The OS usually provides mechanisms to register interrupt handlers - functions that are called upon occurrence of an interrupt. In Linux see request_irq() and friends in linux/include/interrupt.h
2. Memory-mapped I/O is physical memory of the device that the platform's BIOS makes available in the same way you also access plain physical memory - simply by writing to a memory address. What exactly is behind such memory (e.g., network interface config registers or an LCD frame buffer) depends on the device and is usually specified in the device's data sheet.
3. I/O ports are accessed through a special address space and special instructions (INB/OUTB & co.). Other than that they work similar to I/O memory.

There's a multitude of ways to find out what resources a device provies and where the BIOS mapped them. Some platforms use ACPI tables (google yourself for the 1,000k page spec), PCI provides info on devices in a standardized way through the PCI config space, USB has similar ways of discovering devices attached to the bus, and some devices, e.g., UARTS, are simply specified to be available at a pre-configured I/O range that is fixed for your platform.

As a start for understanding Linux, I'd recommend "Understanding the Linux kernel". For specifics on how Linux handles devices and what is there to write drivers, have a look at Linux Device Drivers. Furthermore, you will need to have a look at the peculiarities of your platform and the device you want to drive.

If you want to start an own OS, a UART is certainly something that will be veeery helpful to print debug output, so you might want to go for this first.

Now that I wrote down all this, it seems that your actual question is: How to get started with Operating System design. This question should be highly valuable for you: What are some resources for getting started in operating system development?

The two big power users in most computers are the CPU and the disks. Both of these have capabilities for power saving in Linux. The CPU clock can be slowed down when the system is not busy, and the disk motors can be stopped when no I/O is happening. For a UART, even if you save all of the power that it uses by turning off its clock, it is still tiny compared to the others because a UART doesn't have much logic in it.

Best ways to save power are1) more efficient power supply2) replace rotating disk with SSD3) Slow down the CPU and memory bus