How do I physically work with a hobby motor?

I would suggest you look at some shapelock. Shapelock.com

You can mold any type of mount you want with this. You could also buy gearboxes that are designed to mount on these hobby motors. But as cheap as they are you may want to consider buying some with the gearbox already attached.

Most hobby supply stores have assortments of wheels, sprockets, gears and pulleys for these or you can find them on ebay.

Good luck and let us know what you build.

get some cardboard or even decent paper & push the axle through it without enlarging the hole. You may need to place masking tape to reinforce the hole once you've made it. The idea here is to maintain the accuracy of the centre hole. After this get a pencil & rub it on the paper so as to make a kind of 'picture' of the surface end of the motor, making sure you can see the mounting holes in the picture. You can then use this paper as a template to make a right-angle mounting bracket for it. careful not to use too long a mounting screws into the end of the motor as they may foul the commutator brushes or the armature. I find a good source of tiny little self-tappers in cheap import shops, not available separately but in carefully chosen throw-away cheap plastic toys etc. Just choose yourself a toy with lotsa little screws!

Mounting motors can be a pain. One ugly, but workable trick in some situations is using hose clamps.