Phase 1 : about 50 million years ago.

After death, bodies of the fish often settled to the lake bottom. If they were buried before, they had a chance to be torn apart by scavengers and decomposed by bacteria = a good chance of becoming well-preserved fossils.

Phase 2 : several thousand years later.

Lake deposits build up over centuries, burying the dead fish under thousands of feet of sediments. The resulting head and pressure from overlying layers caused the buried sediments to dry out, compress and begin to change to limestone.

Phase 3 : about 40 million years ago.

Each passing season buried the fish deeper and deeper under the lake sediments. Eventually over 1,000 feet of sediment bury the fish, filling the basin.
Eventually the lake disappears, sediments stop accumulating and erosion begins to remove overlying rocks.

Phase 4 : a summer day in 1989...

Over the course of million of years, the land is uplifted and wind, rain and down-cuting streams slowly erode hundreds of feet of rock. Eventually the sediments of the old lake bed are cut through and exposed in the buttes of Fossil Basin.

The fish are now close enough to the surface to be excavated by paleontologists or fossil collectors  .