Total noob here (never touched Arduino before today), & have pretty much no hands-on technical experience (although with lack of experience, I make up in enthusiasm to learn!)
Question: How do you attach a plate (material of plate yet to be decided, likely stiff cardboard) to a stepper motor? See illustration below:
LarryD's suggestion of a hub is the best answer so far. You can find hubs at ServoCity.
However, there might be a bigger issue: the amount of load the motor can take. A better quality motor will have specs for the amount of axial and radial loads that are acceptable and those numbers are usually pretty small. For most hobby stuff it doesn't matter, but the more general "engineering way" (TM) of doing something like this is to mount the plate to a bearing and then have the motor drive the plate separately. That way the bearing can be as large as needed to support the weight of what's on the plate and the load on the motor is minimal.
You can see this technique if you look at the rotating "lazy susan" plate in a microwave: it's on a plastic bearing that supports the weight of the food, and driven in the center from a motor that's below the cooking area.
Just as your drawing suggests. The motor shaft, if like mine, already has a mark in the end of the shaft so it can be drilled and tapped for the screw of your choice. Your table will need a similar hole drilled so your screw can firmly hold the table to the shaft.
Paul
