Shorting probe tip to ground
I always do this when measuring any fast signals or when the circuit is noisy. Putting the tip to the ground clip should give you zero volts to the scope, but often it doesn't. That is because the potential at the ground point of the scope can be moving relative to earth (or the local reference point of the supply feeding the scope). Even if your circuit is "floating" there will be capacitance to ground. As rapid transient occur at the ground clip point, currents will flow in the probe ground wire. This will in turn generate voltage transients between the ground clip and the actual scope ground. These can be measured by placing the tip onto the ground clip. Any waveform that you observe when doing this will be superimposed on the real signal that you are trying to measure when you connect the tip to some point varying with respect to the ground clip.

If you see high speed transients when using a scope probe, try this test to check if they are due to this affect. This also applies to differential probes, connect the +ve probe to the same point as the -ve one to check that the differential probe is rejecting all the common mode signal.