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 x-axis lead screw for a CNC router. Assembly and concept for the x-screw is the same as the y-screw. The only difference is that you will need to pick up the entire machine and provide access to the bottom.
Just like the other axes, alignment is critical. It doesn't have to be perfect, but pretty close. The coupler that you should use allows a tiny bit of flex since the middle component in the coupler is rubber.