Gearbox design involves quite a few topics. More than should be condensed into one post. I can address your ratio question in this one. (I'm assuming you are starting at the very beginning by the way)
For the purposes of this post we will ignore the existence of the rest of the gearbox in the attached photo (the rest of it should be coming up in CD media soon).
Highlighted/blue gear would be called the output gear and the smaller gear to the right attached to the motor is the pinion. Pinion refers to the gear attached to the power source or the input. Generally the gear ratio is expressed as the number of teeth of the output over the number of teeth of the input, in this case 44/11 or 4/1 or 4:1.
basically every time the pinion spins 360deg it advances 11 teeth and the output advances 11 teeth. 11 teeth = 1/4 of the teeth on the output gear resulting in 1/4 a rotation of it for every whole rotation of the input.
This US Navy video from 2:08 to 4:37 is a great example:
https://www.youtube.com/watch?v=s1i-...jLyVmGXSxTl-KQ Note he exspesses his ratio as input over output or the reverse of what I use above.