Using liquid nitrogen certainly accomplishes the freeze fast bit, and gets some overrun (air entrained in the frozen mixture) from the stiring and from the nitrogen itself. Unless you've got a friendly cryogentics facillity or chemist, it's rather hard to get small volumes of liquid nitrogen.
Putting the bowl in the freezer and stirring every hour or so is easy. It doesn't produce terribly good results, though. It'll tend to have big ice crystals in it, won't freeze as hard as you'd like, and takes a long time.
Another method -- and the one I use -- is to put a small volume of base in a large ziplock bag, and then put the sealed bag into a salt/ice mixture. I use about a pint or pint and half of base into a two gallon ziplock, which goes nearly flat (so as to maximize the surface area exposed to the ice/salt. Squeeze all the air out, too.) onto a bed of ice, and then is covered in more ice/salt. Let sit for 20 minutes or so, take out of the ice, knead the starting to freeze mixture, put back in the ice for another 20 minutes. If you stop before it's solidly frozen, you can put the ice cream in a more elegent container. If you don't, you may have to slice the bag open to get it out.