I can try, with one example. Lakes, under some conditions, can have a fairly thick layer of oxygen-free water near the bottom, while supporting plenty of life up near the surface. Microscopic organisms like diatoms and coccolithophores can grow very well up top, with their shells, as well as silt and clay brought into the lake by streams, providing a continuous source of sediment that rains down through the "anoxic" layer. Any larger creature (like an archaeopterex, fish, or insect) that happens to die and sink into this oxygen-free sediment will be largely protected from rotting away - no predators or scavengers can live without oxygen, and the only bacteria that do live there are pretty slow eaters, so to speak. So the animal remains will be buried by sediments, with at least a good shot at traces being preserved. If the sediment in question eventually gets buried enough to become rock, and then gets unburied enough for someone to find it, we have a fossil.
There are fossils known from such things as volcanos - Pompeii comes to mind - but many more are known from rocks that show no sign of any violent event while they were forming. A lot of the fossils out here where I live, in fact, are remains of reef-dwellers, that could only have lived in clear, calm, shallow water. And a reef 500 meters thick could have only grown a millimeter or two at a time, as the "foundation" it was on slowly sank relative to the sea it was growing in - otherwise you wouldn't find the fossil sponges and such that lived there rooted in their growth positions.
So to answer your question: the field of taphonomy is the study of how fossils form, and it has long since established that processes that aren't cataclysmic are responsible for many (nearly all?) fossils.
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