Holleigh,
Check out the link below. The first and second illustrations are passive systems, what you need, perhaps? The third is an active system without electricity.
Good luck.
Ed

Here is a link that might be useful: Systems

You can start your plants in straight water, & some such as lucky bamboo will work, but others will eventually need nutrients. Some orchid growers propagate this way.

The easiest method is to get a saucer for the pot & water it from the bottom. The second easiest method is to get a wick, insert it in the media, down into the saucer & again water the saucer. You can use a rope, or find wicking material at a fabric store. The wick can develop algae, however.

One problem you may have is keeping the clay moist so your plants do not dry out:

There is a replenishing system at this link:

http://forums.gardenweb.com/forums/load/hydro/msg0319192726254.html?6

If you put your plant in the bottom pot, the dripping of the water would help oxygenate it.
Before pumps were used in hydroponics, water was aerated through dripping devices.