Originally, the rotation rate of a planet was measured by tracking visual features believed to be on the surface of the planet. This is still the case today for nearby rocky planets with solid surfaces and distinct landforms visible from earth.
A different way of tracking the planet's rotation is by bouncing radar signals off the planet and measuring the Doppler shift in the returning signal. This method is especially useful when the planet is too close to the sun to be easily observed and additionally has very low contrast surface features, as is the case with Mercury.
To accomplish this, a radio telescope sends out a short electromagnetic pulse of known frequency and then records the spectrum of the returning echoes. By the time the signal reaches the other planet, it has spread out to cover the entire planet, so the echoes return at different times. The echo from the sub-radar point, the closest point between earth and the other planet, will be the first to return: it will show no frequency shift other than the known orbital frequency shift. All the other signals bouncing off other parts of the planet will return slightly later and include a rotational Doppler shift, which can be compared against the sub-radar baseline to determine the rotation rate of a rocky planet.
Measuring the rotation of gas giants is much more difficult. Not only are surface features not visible from outside the atmosphere, but the gas giant may not even have a solid surface beyond a possible rocky core. To make things even more interesting, different layers of the gas giant may rotate at different rates. Most rotation rates for gas giants are bulk rotation rates rather than surface rotation rates for a rigid body.
Thus far, the approach that has worked best for three of the four gas giants of our solar system is to infer a planet's bulk rotation from the rotation of its magnetic field.
Saturn is proving a challenge, however. When the Voyager probes flew by Saturn in 1980 and 1981 respectively, radio emissions suggested a period of 10 hours and 39.4 minutes; yet when the Cassini probe reached Saturn in 2004, it found that the radio rotation of Saturn was 10 hours and 45 minutes, with an uncertainty of under a minute.
It is now believed that Cassini picked up on radio signals connected with convection of the plasma disc rather than on a rotationally-linked radio source. Another newly discovered complication is that geyser activity on Enceladus, one of Saturn's moons, may be creating electromagnetic "friction" which slows down the magnetic field rotation relative to planetary rotation.
Based on all information gathered by the probes, the compiled estimate of Saturn's bulk rotation is now considered to be 10 hours, 32.6 minutes.
A common alternative to determining bulk rotation in gas giants is to assign local rotation rates to stable regions and layers. The newest research involving Saturn's rotation uses atmospheric dynamics to attempt to infer that rotation. By this method, the rotation rate of Saturn's System III region is 10 hours and 34.2 minutes: nearly two minutes shorter than previously thought.