How do these dripping rock shapes slowly form in caves?

Water dripping for a long time, leaving behind tiny bits of mineral each time, is correct — that slow dripping is how these pointy stone shapes, stalactites, build up drop by drop over thousands of years.

Bats don't build these out of mud, and they don't fall from the sky during storms — just fun-sounding guesses, not how caves actually form these rocks.

Shapes hanging from the ceiling are stalactites, while ones growing up from the floor are stalagmites — a trick to remember which is which: stalactites hold 'tight' to the ceiling.