Volume is measured by some unit cubed. The unit depends on where you are. In Canada and Great Britain, cm^3 are used. In the United States ft^3 is the normal unit of measurement. But in all three countries there is a familiarity with the units used in the other 2.
Volume is a length and width for 2 of the dimensions used to measure it. Length and width are what you see on the flat of your screen. Depth is a measurement that comes out at you from the screen or it goes from you.
Usually to measure it, again depending on where you are and how big the unit you are measuring, is for most people a matter of finding a tool that will do the job. If you want to measure anything on a sheet of paper, a 12" ruler will do which is about 30cm long. If you want to measure the length of your house a tape measure is an ideal tool.
If you want to measure the distance from Earth to Venus much more sophisticated methods much be used: certainly a tape measure would not work.