Intel 4th Gen. Stock Cooler
The cooler consists of 7 main parts. The main mounting frame holds the fan and heatsink in place and secures to the motherboard. The fan blade blows air across the heatsink. The heatsink is a circular aluminum array of fins which distributes the heat coming from the CPU to be blown by the fan. The heatsink contains a copper core press fit into its center which interfaces with the CPU's IHS (integrated heat spreader). Four pairs of twist-locking plugs and pins snap the assembly onto the motherboard. Finally, the motor sits inside the fan blade's center and fixes it to the mounting frame.

Disassembly
Many of the components in the overall assembly here were fixed with joining methods intended to be permanent, making disassembly challenging.
The locking pins and plugs were inserted into each other and the mounting frame with one-way snap fits. I was able to separate a single pair from an additional cooler I own by cutting into the mounting frame. I was unable to separate the motor, mounting frame and fan blade from each other though as they are fixed together with a permanent adhesive.
Bill of Materials
A bill of materials is shown below with the accompanying labeled subassembly images shown to the the right:

