As the story goes, about 1.5 bya (billion years ago), after some oxygen producing monerans changed the earth's atmosphere and killed off most of their neighbors, protists developed. Protists are defined as single-celled organisms which have a real nucleus. They're almost everywhere water exists on planet earth.
Protists weren't always so easily recognized. Originally, most protists were placed in either the animal or plant kingdoms, byt they're just too darn different to be grouped so easily. Besides, how do you group a critter that moves independently, can function like a wee animal, but can make its own food like a plant? The had to make a separate kingdom.
Actually, most protozoans don't resemble each other very closely. It seems like scientists threw them together in the same kingdom because they didn't know where else to stick them. This kingdom has undergone a lot of revision and reclassification. This is because scientists are discovering new ways in which creatures are related.
Scientists aren't in total agreement how the kingdom should be broken into phyla. At least not the scientists I referenced. In researching for this page, the most common organization was a division into several phyla:
Other pages I went to had oodles more divisions than this. This doesn't mean a whole lot to anyone but the biologists who study these things. For the sake of understanding, let's group protists into three categories. We'll call them the animal-like protists, the plant-like protists and the fungi-like protists.