Well, for an external filter, you would need a U shaped pipe to draw the water out of the tank, and into your filtration system.
Then you would need a waterproof box of some sort, and either a lip on it, or a funnel sort of attachment, to let the water go back into the tank.
Most external filters put their motor right below the U shaped tube, to suck the water in, and through the various filter media.
Air powered filtration systems usually have an air pump, a thin air tube, and a bubble stone beneath an uplift tube. The bubbles in this tube cause the water to rise along with them.
You can't put the air tube into the U shaped tube, because the bubbles would block the tube at the elbow. I suppose you might use a J shaped tube, but I don't think the bubbles would push the water hard enough to get it over the lip of the aquarium. Thus, you would probably need to put an uplift tube in the filter box itself. However, external filters generally need to have their water level a good deal higher than the water level of the tank, so unless your air pump has the strength to power a small sauna, I don't see how it would work.
I'm also a little confused about a pump "not run by electricity" Are you hoping to have the movement of the water in the tank power it, as a perpetual motion machine?
I guess a powerful clockwork spring, or some massive counterweights might be pressed into service, but this would require specialized watertight fittings, unless you want to run a belt into the water, and back out...
I dunno about the motor. Most of the professional filters just have a sort of paddle wheel, so I guess it's not too hard to make. For the housing, I suppose you might press an old cardobard milk carton into service, and a snorkel might do for the U shaped tube.
Pet stores generally have pretty cheap stuff, I've seen a few nice off the shelf extrenal filters that'd work pretty well for a few gallons, and by the time you factor in materials, and time, you may do better that way any how.
OF course, that wouldn't be DIY.