I don't know how useful it is, but what's important here is the fact that we accidentally ingest cysts of Blastocystis, and we shed cysts that can be passed on to other hosts. The cyst stage is the transmissible stage, and the way the parasite can survive outside the body; we don't know for how long cysts can survive and remain infective. In our intestine and triggered by various stimuli, the cysts excyst, transiting to the non-cyst form, which could be called the trophozoite / "troph" stage, or to use a Blastocystis-specific term, the "vacuolar stage" (many stages have been described for Blastocystis, but I might want to save that for later!). This is possibly the stage in the life cycle where the parasite settles, thrives, multiplies, etc. You can see a picture of vacuolar stages in this blog post. Many protozoa follow this simple life cycle pattern, among them Giardia and most species of Entamoeba. If the stool is diarrhoeic and you are infected by any one or more of these parasites, it may be so that only trophozoites, and, importantly, no cysts, are shed! This has something to do with reduced intestinal transit time and, maybe more importantly, the failure of the colon to resorb water from the stool which means that the trophozoites do not get the usual encystation stimuli. Importantly, trophozoites are in general non-infectious.
There is documentation that once colonised with Blastocystis, you may well carry it with you for years on end, and as already mentioned a couple of times, no single drug or no particular diet appears to be capable of eradicating Blastocystis - this is supported by the notion that Blastocystis prevalence seems to be increasing by age, although spontaneous resolution may not be uncommon, - we don't know much about this. Now, although day-to-day variation in the shedding of Blastocystis has been described, it is my general impression that colonised individuals may shed the parasite with each stool passage, and well-trained lab technicians/parasitologists will be able to pick up Blastocystis in a direct smear (both cysts and trophs may be seen). To do a direct smear you simply just mix a very small portion of the stool with saline or PBS on a slide, put a cover slip over it and do conventional light microscopy at x200 (screening) or x400 (verification). Very light infections may be difficult to detect this way, and if you don't have all the time in the world, a direct smear may not be the first choice.
The "king" of parasitological methods, however, is microscopy of faecal concentrates (Formol Ethyl Acetate Concentration Technique and any variant thereof), which is remarkable in its ability to detect a huge variety of parasites. Especially cysts of protozoa (e.g. Giardia and Entamoeba) and eggs of helminths (e.g. tapeworm, whipworm and roundworm) concentrate well and are identified to genus and species levels based on morphology. The method is not as sensitive as DNA-based methods such as PCR, but as I said, has the advantage of picking up a multitude of parasites and therefore good for screening; PCR methods are targeted towards particular species (types) of parasites. A drawback of the concentration method is that it doesn't allow you to detect trophzoites (i.e. the fragile, non-cystic stage), and, as mentioned, diarrhoeic samples may contain only trophozoites and no cysts...
In many countries it is very common for people to be infected by both protozoa and helminths, and in those countries microscopy of faecal concentrates is a relevant diagnostic choice. In Denmark and many Western European countries, the level of parasitism is higher than might be expected (from a hygiene and food safety point of view) but due to only few parasitic species. Paradoxically, the intestinal parasites that people harbour in this part of the world are parasites that do not concentrate well. They are mainly: