Cwalker, that is a good question. There are a couple of ways. I use a combination of two ways. I use the plastic boxes that you can buy at the the dollar stores with the lids. Since those same boxes are here to carry the models to a show in, and to cover a model to keep the dust out, I use them upside down to enable stacking the models as I build them.
I also have a home made working station/spray booth with a flip up glass cover over the front. I either set the model on a card and pop it into one of the side bays, or into the above stackable boxes and into the side bays. This doesn't add any extra effort, because ever since I got dust into an airbrushed paint job, I have been very serious about keeping models covered as I work on them, transport them, or display them.
On my bench, it is possible to have a model in a box sitting just a few inches away from the model I am currently painting. I also use assembly jigs made from Legos for my models,,,,,those can slip into one of the cubby holes also. Small parts are still attached to sprue tree stubs and in "bead baggies" from the crafts section, labeled for the model they came from (when I remember to do that, that is) I paint small parts while clamped in copper alligator clips squeezed onto a finishing nail poking up through small squares of balsa wood,,,,,,,those also can stand in the model cubby/booth.
all of this lets me model right next to SSgt Anne if I choose to, spraying Acrylic paints as I go along.
Rex