hi,
leakage current is defined as the current that "leaks" between drain and source (D/S) of a MOSFET when the device is OFF, i.e, its Vgs is below the device threshold voltage. In most case, when the leakage is mentioned, it is referring to Id current.
However, you can also see terms as "gate leakage" and "body leakage" which refer to the current that leaks through gate of the device into the channel of the device, and from D/S junction to the body of the device respectively. The D/S leakage is much more important than the Gate and Body Leakage, therefore usually the term leakage current is referring to the D/S leakage when the device is off.
The measurement depends on what are you measuring. If you are talking about measuring lekage current of a given chip, one should observe the current drawn from power supply while the chip is in idle mode, assuming in the idle mode no parts of chip is ON and there is no static current path.
Two important points about leakage are that the leakage current of a MOSFET increases with decreased channel length, since the electrostatic control becomes worse. It has also an exponential variation w.r.t to temperature, so it drastically increases with temperature. In large designs manufactured with most advanced technology nodes with many small length transistors, power consumption due to leakage currents can be as important as dynamic power consumption.
Hope that it help.