The nitrogen cycle: not to worry if you didn't pay attention in chemistry class
Very simply put, fish waste and vegetative debris (from pond plants, tree leaves, turf runoff, etc.) produce toxic ammonia. Bacteria added to the water converts the ammonia to nitrites; a secondary bacteria turns the nitrites to nitrates (a much less dangerous component) which is then utilized by the plants as fertilizer or off-gassed to the atmosphere as nitrogen. The cycle then begins anew.
The parts of the filtration system
The skimmer's job is to contain the pump and catch the bulk of the floating debris. It generally has an easily removable basket or net, for leaves and such, and filter mats (a material similar to that used in your home furnace and air conditioning system) to retain the smaller debris and also provide somewhat of a home for the beneficial bacteria to colonize upon. You want to have a box with an easily removable top for access to the pump, net, and filter media.
The biofalls provides the structure for the top waterfall, does the initial aeration for the circulating water column, and contains the largest amount of breeding surface for the beneficial bacteria. A very common medium is a form of lava rock, a very porous material generally kept in a mesh bag for easy convenience in cleaning. (Other media -- plastic balls, etc. have also been used as bacteria incubation devices.) This is the location where most of the ammonia biological conversion action takes place, although the stream boulders and gravel on the liner itself also offer a substantial safe haven to the bacterium.
For the non-mechanical parts of the system: fish eat algae, thus helping the bacteria to do its job in controlling the green menace; the perennial question is how much and how often to feed them? A good guideline is to underfeed rather than the opposite; feed them as much as they will eat in about 3-4 minutes, and not more than twice a day. If they leave food on the surface, you've given them too much. Clearly, some experimentation is called for in the feeding aspect. Don't worry, they won't starve while you do the testing.
How many fish? Many fish enthusiasts use a ball park figure of one inch of fish for each 10 gallons of water. Here's another way to look at it. The fish count is probably the most difficult analysis to make in working to enjoy a pond with good clarity, and it's more art than science.
Not technically a part of the filtration system, the pump's volume of water put through the system is important in reducing algae formation. Stagnant or slowly flowing water is conducive to algae formation; that's reasonably intuitive, don't you think? A good rule of thumb is to have a pump with sufficient capacity to circulate the pond water every two to three hours. Look here for a good calculator.
The boulders, rocks, and gravel in the feature
Beneficial bacteria like rough, irregular areas on which to colonize. It stands to reason, then, that the more rock under the water's surface, the better. Aside from reducing UV degradation of the liner, boulders and gravel on the liner provide a convenient place for the bacteria to call home. Covering the liner above the water line stabilizes the liner, precludes shifting when the pond is filled, and keeps the sun from beating up on the EPDM.
Aside from the fact that pond plants are just neat looking, they help to purify the pond water by absorbing the undesirable nitrates from the water column; additionally, when properly selected and planted, they convert atmospheric carbon dioxide to help oxygenate the water.
Even if you don't intend to stock your water feature with fish, you should strongly consider the inclusion of plants. In an open water pond they can help shade the water to retard algae growth (use enough to shade 50-60% of the water's surface). In a pondless stream, marginal plants are of great help in keeping the water clean and will make great accents even if they don't float.
Decision time: open water pond or pondless waterfall
With regard to water quality, it's tough to make an easy decision on the best choice. Open water ponds usually have more water volume to facilitate the growth of algae, but it's easy to scoop junk like string algae from the surface. Pondless features, because they generally use more rock and, thus, have more available interstices (another word of the day) in the rock, are able to colonize bacteria more easily.
You can walk on the pondless basin to pick up debris which might eventually degrade into a water quality issue; you can't do that with an open water pond (at least most of you can't). If you're a fan of UV sterilizers (say it ain't so), a pondless is likely not for you.
At the end of the day, the choice is certainly yours; the one non-water-quality factor that usually influences the decision-making process is the safety that a pondless water feature provides. And, of course, it's really fun to "walk on the water."
Very cool ponds!(click thumbnails to view gallery)