Small microscopic visible particles move randomly around in water.
If water were continuous, this shouldn't happen.
The amount it moves also quantitatively matches with the expected properties of water.
Tiny uniform plastic beads called "microbeads" are the preferred 2019 modern method of doing this: https://en.wikipedia.org/wiki/Microbead
Original observation in 1827 by Brown, with further experiments and interpretation in 1908 by Perrin.