If I wanted to power 10 switch machines, how big of a 12v supply would I need?
A regular DC power pack that you run your trains on should do it. Or about 1 amp.
All at the same time?
Atlas switch machines only need power to throw. you probably only need to power one (or two perhaps at once). After that they draw no current. They do need a hefty jolt to move. 1 amp will do it. You should consider a capacitor discharge unit. (do a search).