The Moon's gravitational force exerted on the Earth's tidal bulge results in a net torque opposite the direction of Earth rotation, pictured very nicely in the below wikipedia graphic.
The Earth's rotation rate is gradually decreasing due to this tidal interaction with the Moon. In order for the angular momentum of the Earth/Moon system to be conserved, the Moon's orbital momentum has to increase, which also causes the Moon's orbital distance from the Earth to increase. This theory of tidal torques explains the tidally locked systems in our Solar System, including the tidal lock of the Moon to the Earth (the Moon's rotation time is the same as it's revolution time).
The rate of deceleration of the Earth's rotation is so small that it can't be easily measured real-time. In fact, over the short time, changes in atmospheric and ocean currents can temporarily cause the Earth's rotation to speed up!
However, over the long term, the minor changes to the rotation rate even out. And the fossil record supports the theory of gradual deceleration of the Earth's rotation! From Deines and Williams 2016:
Similar to using tree rings, various sea creatures have daily as well as yearly (seasonal) deviations that can be used to tell how many days are in each year, and hence how long a day is at a particular geologic time. To quote their paper:
Early paleontological papers dealing with geochronometry concentrated
on corals, bivalves, and brachiopods, which have general daily growth
increments that indicate annual variations. With successive alteration
of daylight and darkness, growth occurs faster during daylight. Annual
variations could be due to changes in daylight length, water
temperature, or even food supply. Shorter periods are found within the
annual variations, which can imply seasonal fluctuations or lunar
synodic months. Variability in specimen growths was verified in recent
animal growth tests. Although the fossil record was reliable, it did
require many samples or long, continuous growth histories to get
better estimates for Earth's rotation rate in ancient times.
It should also be noted that the Earth's rotation is slowing due to similar tidal interactions with the Sun, though these effects are much smaller than those due to the Moon.