Dinoflagellates (including parasitic Piscinoodinium) often get classed among algae, under the misleading impression that any single-celled photosynthesizer must be some kind of alga. Only about 200 species have managed the transition from marine life to fresh waters, but a few common species undergo periodic blooms that impart fishy tastes and smells to drinking water.
They are unicellular organisms, sometimes bound in armor plates of cellulose that have fantastic and beautiful shapes. Their motile stages move by vibrating their two whiplike flagella, one of which lies in a crosswise groove and imparts a revolving twist to dinoflagellate movement. They encyst in the detritus on the substrate. In lakes, photosynthesizing dinoflagellates form a significant part of the green trophic base, though not all dinoflagellates are capable of photosynthesis. Some dinoflagellates hitch rides on larger creatures, such as copepods; others, like "Ooodinium", are actively parasitic.
Dinoflagellates have complicated life cycles that may include a resistant cyst that helps them disperse even into isolated or temporary waters. They are certain to be present in small numbers in the aquarium, though you'd need a pretty good microscope to catch a glimpse, they are so small. Not all dinoflagellates are microscopic, however; Noctiluca scintillans, the "scintillating nightlight," a phosphorescent marine dinoflagellate that may coat every dip of the midnight oar with a shower of greenish sparkles, can get to be a couple of millimeters across and attack fish eggs.
Dinoflagellates most often come to public notice in connection with notorious "red tides" in polluted coastal saltwater. (The red color actually comes from an alga that blooms with the fish-killing dinoflagellate in those unnaturally enriched waters.) Though 90% of the world's dinoflagellates are marine, there is one group of parasitic freshwater forms, the oodiniids ("oh-uh-DIN-ee-ids"): Oodinium, technically Piscinoodinium, sometimes troubles us by feeding on fishes' skin and gill surfaces. When you hear about a "parasitic alga," it's Piscinoodinium they're talking about. It can get some energy from photosynthesis while it waits for a host fish to settle on. The combination of chlorophyll and carotenoids in individual Oodinium's chloroplasts gives the parasite colony its familiar golden color.
Links. Andrew MacRae's good brief introduction to dinoflagellates, with some electron micrographs, is at the Dinoflagellate Page, hosted by U. of Calgary. Another page introducing dinoflagellates is the UCL Microfossil Image Recovery page.
The U of C Berkeley site has good material on dinoflagellate roles in the ecology of marine waters.