"Infusoria" was the old-fashioned aquarist's quaint expression for a dense culture of water-borne protozoans of the freshwater plankton, especially rotifers and ciliates such as paramecium but including flagellates and amoebas. The name for these "animalcules" was given general circulation by Christian Gottfried Ehrenberg's Die Infusionsthierchen (1838). An infusion is a watery solution produced by steeping or macerating vegetable matter; the summertime "sun tea" you brew out on the deck is an infusion. "Infusoria" populations bloom in infusions of manure or decaying vegetation. The most nutritionally desirable of the planktonic protists are probably rotifers, but the ciliates also provide good nutrition for larval fish.
"The greatest problem in fish culture is the first food," wrote Mr Innes long ago, with the emphasis of italics. Infusoria (and green water) form the first foods for the smallest fry, like gouramis, barbs and characins. Those larval fishes are too small yet to handle newly-hatched brine shrimp nauplii, the mini-daphnids called Moina or Turbatrix vinegar eelworms.  
There's no point feeding anything until the fry have absorbed their yolk sac and are swimming free; you'd only cloud their water. Though you can't see what they're after, feeding fry make characteristic jerky dashing motions, and well-fed fry have bulging bellies. For fastest, sturdiest growth, you'll want to move on from infusoria to the nematodes or nauplii as soon as the fry can handle them, feeding both foods for a few days to help the stragglers keep up. 
Paramecium. The most familiar among the infusorian ciliates is paramecium, the "slipper animalcule" you might remember from High School Biology.  Paramecia multiply mostly by fission, with a little sex on the side from time to time. This flexible strategy helps them multiply very fast, so your culture will be mature in a matter of days.
Paramecia and other non-photosynthesizing single-celled planktonic creatures feed on bacteria that are breaking down organic substances. So to culture them, you need to supply some decaying organic material, and to be patient for about four days' time at temperatures in the low 80s. The "infusoria" culture you're after is no more than a productive concentration of the same "cloudy water" problem you avoid in the show aquarium. When similar plankton appears unbidden as a white bloom, especially in a new tank, we treat the phenomenon as a problem instead of a food culture. Ciliates and other microscopic plankton are always present in a mature aquarium, but in comparatively sparse numbers. They form an important link in the food web.
Culturing. Requirements for a ciliate culture, or "infusoria," are simple: a starter culture plus organic nutrients, exposed to strong daylight (but not sunlight) and warmth (83°F is the ideal), at a stable and somewhat alkaline pH above pH 7.0. You'll want water that is already rich with abundant founder populations of the organisms you're after, rather than dechlorinated tapwater. The starter can be filter-sponge squeezings in water from a well-established planted aquarium that hasn't been medicated recently. Or water from a fishfree plant nursery tub. Even water from a flower vase, as long as there were no additives in the water, would be more productive than raw, de-chlorinated tapwater. You'll want a glass or clear plastic container, so that you can judge your culture, with a wide mouth for maximum air/water surface. The mature culture should be cloudy but not milky-opaque, with a ripe "pond" odor but not a foul bacterial stink. Nevertheless, your family will really want you to keep a paramecia culture covered with a sheet of glass or plastic food wrap. Culture water that is too rich in organics, combined with not enough aeration, will simply encourage bacterial fermentation, which isn't what you want. My own soft water needs a shallow layer of crushed coral to keep the pH above 7.0.
Organic nutrients spark the bacterial decomposition that forms the base of this rough-and-ready ecosystem. So you'll need to add some vegetal matter. Hay softened by boiling was traditional. Rotting leaf mold, rabbit droppings, powdered cereal or instant mashed potatoes, baby food or hardboiled egg yolk crumbs, or stale fish food— they all work. Wilted lettuce leaves left in the dry air till they're brittle, then crumbled, would be my first choice.  Not all the generally recommended media are what you want: even oil-free lawn clippings may be contaminated with garden chemicals, and banana skins and sliced potatoes tend to encourage a lot of fungus, in my experience. If I were already running a DIY CO2 setup, I might add just enough filtered yeast culture to faintly cloud the water.
Snails in the culture are good. (Aren't some Ampullariid Apple Snails even called "Infusoria Snails?") Their droppings encourage the protists, and the snails act like canaries in a mine shaft: when my Melania snails crawl above water level, it's high time to re-culture!
Commercial fry liquids. You may think you can skip this first stage by feeding the fry with a commercially-bottled liquid fry nutriment. These liquid fry feeds get very mixed reviews from experienced fishkeepers; one group states that whatever good such products are doing is possibly in providing a source of decaying substrate for bacteria, which in turn feed the culture of protozoans that you're really after. Well, that's still a perfectly accptable reason for buying the liquid fry food. In fact, a few drops of skim milk or liquid fry food are often recommended in culturing paramecia.
Another substitute: Grindal worm contaminants.  When my Grindal worm cultures have been fully mature for a few weeks, the damp culture medium I use (coir, ground coconut shell) begins to teem with nematodes and even more minute competitors of the worms: before long the culture will doubtless crash.  In the meantime, when I rinse the Grindal worms into a jar to settle, the water above them is cloudy with protists from the film of water that surrounds each particle of coir. Ordinarily I pour this off and top up with clean water, letting the worms settle again.   I find that Betta fry batten upon this rather unselective  but pasrasite-free by-product of Grindal worm culture.  I never add more than 2 to 4 oz. in a 10-gallon tank, not enough to remotely cloud the water.
A well-established plant nursery is often the easiest place to spawn fishes and raise the fry without shifting them in a pipet. The "infusoria" populations are already there, especially if you've been lax lately about removing yellowed leaves. During the two or three days following egg-hatching, while fry are absorbing their yolk sacs, a pinch of powdered yeast encourages infusoria without favoring the development of egg-fungusing Saprolegnia
Links. There are rigorous laboratory directions for culturing paramecia under sterile lab conditions in "The Zebrafish Book: a guide for the laboratory use of zebrafish," which is part of information for biologists deciphering the zebrafish genome at the Zebrafish Information Network. Don't be too proud to look through "Zebrafish for K-12" also. In the lab culturing directions, you use distilled water, a brewer's yeast tablet, boiled wheatseeds (the "wheatberries" of your local healthfood store) and a seeding from a good clean young paramecium culture, all stored in strong light (not sunlight) and ready in 4 days at 28.5°C. That would be 83°F. You may not go about culturing so meticulously, but isn't it good to know the ideal temperature of a paramecium culture?
Charlie Grimes' simplest possible recipe for culturing a mix of Euglena and paramecium (the commonest kind of free-swimming ciliate) in Aquarium Fish, April 1997, required no more than a gallon jar of clean aquarium water and a dried pea! It has never been quite that simple for me. In his former website Mike Edwardes suggested putting a slice of boiled potato in some rich old tank water, incubated in a brightly-lit window till it's cloudy with bacteria. He suggested continuous light aeration, as low oxygen levels inhibit aerobic bacteria. As the water clears, the protozoans are at their most numerous— in 3 or 4 days.
Francisco Borrero had this "boiled greens" technique from his mother, a commercial breeder of danios and other egglayers:
"This is the best way I've found of producing good infusoria cultures for feeding small fry: I take several spinach leaves, any variety, and rinse them very well. Spinach, collard greens and probably others work just as well. Best but not strictly necessary is to use organic, or certified as with no pesticide. If it is not fresh it does not matter and may be even better. Put in a pot (I prefer a glass pot) and bring to just past boil. Turn off inmediately after boiling temp, or even just before.  Let this green water cool to room temp. I do this by placing it outside on the porch, uncovered. This may help innoculation.  Use as a food for infusoria cultures. If you let it sit in a wide mouth jar for a couple of days, it will "develop" infusoria. (quotations intended to avoid suggesting spontaneous generation, which of course does not happen). What I really do is to innoculate a fresh batch of cooled green water with a small amount of infusoria innoculum taken by pipet from a rich infusoria culture produced in the standard manner. Wait 1-3 days depending on temperature. The result is much cleaner, denser and longer-living infusoria cultures than with standard methods. This method results in the virtual absence of the nasty bacterial decay film which is bad for fish fry, and bad for the infusoria culture. After producing the first culture by the lettuce green water method, I use this as an innoculum for suceeding batches. I start a new jar every 3rd day or so, allowing having constant supply of clean cultures. Start with clean jars. Soap residues in jars will result in slow or no culture happening."
Richard Pon's "Paramecium culture" notes for the Calgary Aquarium Society begins meticulously with a purebred paramecium culture obtained from a lab, cultured with wheat grains and brewer's yeast.
Adrian Tappin"s "Feeding Rainbowfishes" section at "Home of the Rainbowfish" has some further culturing techniques. Aquaculture Supply (with a link to their "") will sell you greenwater and plankton culture kits, with the famous and universally-recommended Plankton Culture Manual by the founders of Florida Aqua Farms, Frank H. Hoff and Terry W. Snell .
Feeding. The trick with feeding from a culture or innoculating a new one is getting a rich dropperful of paramecia without too many bacteria. Don't just add the whole culture to the fry tank: it's mostly water, contains too many bacteria and often there's a scummy lipid layer at the culture's surface you'd also particularly like to avoid. Ideally, you'd like to keep a steady supply of ciliates and rotifers available to your larval fishes, without actually culturing "infusoria" right in the fry tank. Try this: as the culture matures, the bacteria will use up most of the oxygen as they work on decomposing the organic substances. First, turn off any aeration you may be using. The resulting lowered oxygen levels throughout most of the culture will encourage the protists to gather after some hours in a shimmering milky layer in the only place where the stagnating culture medium contains some oxygen diffusing in from the atmosphere— just under the surface. From there, you can draw them up in a plastic syringe or a large eye dropper.
Alternatively, you can extract some paramecium culture in your "aquarium only" turkey baster and fill a tall narrow bud vase. After ten hours or so, you'll have a clean concentrated layer of ciliates at the top of the vase. With an eye dropper, you can remove them, either for feeding fry...
...or for seeding a more selective second culture of infusoria. The first culture you develop, using rich old unmedicated aquarium water, may prove to be less than select. But draw out some culture from the paramecium layer and re-culture that. Since paramecia multiply so quickly, they will outpace other plankton in the re-cultured medium. You'd better keep a couple of infusoria cultures going while you need them, because nothing crashes more unexpectedly than populations of protists.
By the time you're considering re-culturing infusoria  a second time, your fry should be ready to move on to bigger prey.