Motor gearing and screw pitch?

[viroy]

Hello all,
I am getting ready to build my very first CNC machine. The one i am going to make first will be just a 2 axis laser cutter/engraver. The laser itself is very lightweight and power rating is under 2w. i plan on moving the laser head, not the table.

I have extracted some stepper motors and a servo from printers that i believe will work fine since the laser head is very lightweight.
After i complete this one, i will be building a much stronger 3 axis machine with a drill.

My question is:
I dont know how to acurately connect the motor to the drive plain for physical movement. I read about people using a certain pitch screw and setting the steps to 1:8 or whatnot. i dont know how to connect the motor to a belt and achieve precisesly measured movement. so what do i need to know to make sure the CNC program (i want to use mach3) is matching with the distance of movements?... if i get code generated to cut say a 2"x2" square... how do i match that up so that 2" in the program really does equal 2" of movement of the laser head?

seems to me if i use the wrong size gear wheel on the end of the stepper motor, i will not be able to get the desired movement measurements.
im geussing theres some simple math to calculate this?

Sorry if im being confusing, this is a bit new to me so i dont know how to properly reference things.
Any help is appreciated

[viroy]

also, i dont fully understand what mechanisms are available for connecting the motor for an axis. i hear of rack and pinion, belt drives... and i guess i dont know what else is available or why i would chose between one or the other