reducing that to make the arm rotate once a "year" (this drive is not shown)
keeping the Moon orbit plane parallel to itself, i.e. to something fixed to the base and not the arm
reducing the Earth's rotation to make the Moon rotate once a "month"
The image shows only three of the drives, the arm's drive is on a separate page (to come). Gear wheels have their number of teeth marked next to them.
Moon Orbit Orientation
The main turntable is at the bottom left. It is fixed to the base. The 56 teeth on its outer rim are used by an 8-tooth gear and two sets of conical wheels (red colour) to transmit the arm's position to the second turntable, the Moon orbit table. This second table will then turn relative to the arm so as to keep a fixed orientation in space. That was the main problem in constructing the orrery.
Moon Orbit Inclination
The Moon's orbit is inclined relative to the ecliptic, so we need a universal joint and a third turntable, fixed to (but at an angle) the Moon orbit table. That is the turntable at the top right.
Turntables have two parts, the top of the Moon table must rotate once a "month" around the Earth. The Moon drive, fixed to the Moon orbit table, takes the Earth's daily rotation and reduces it (24/8)×(56/8)=21 times to simulate a "month".
As a side effect, the Earth's axis is inclined to the ecliptic as well, but at the same angle as the Moon's orbit. In reality the two inclinations are different and their orientations in space too, but for the purpose of the orrery this is not important.
Main Arm Drive
The main arm drive takes the daily rotation of the Earth from the driven axle, reduces it by a factor 288 and then pushes the main arm around on its special vertical bearing on rubber wheels.