A CNC router machine is probably the most useful tool a hobbyist can own, but the price for a CNC machine on the market is way more than the average hobbyist is willing to spend. You can build your own CNC with very basic tools, little knowledge of machinery, mechanics, or electronics, but be warned, these machines are inherently dangerous, so wear the proper protection and use common sense. At the very least, read the instructions and precautions on every tool you use.
Now, a CNC stands for Computer Numerical Control, but that is gibberish. It does hint you to the fact that something is controlled, and probably by a computer. It's really a mechanism that interfaces to a computer to control its movements, similar to a robot, but this machine has a specific function. It cuts or shapes things with this control. In essence, a computer precisely controls a cutting tool, like a router for instance, to cut materials such as wood, plastic or metals into shapes only bounded by your imagination.
This video tutorial will show you how to make the z-axis motor mount for a CNC router. This video demonstrates the wrong and the right way to mount the z-axis motor. It starts out with a small piece of wood about the size of the motor front plate, but wider so two mounting screws can be affixed to the y-axis top bearing support. Drill the hole in the middle for the shaft and position the motor on the piece to mark for the mounting holes. Drive nuts into the holes for holding strength and place the piece onthe z-axis and drill two more holes to hold it in place. Sounds simple, right? Well... you'll see. The moral of this story, watch the complete video before getting started, just like the teachers said in school.