Displacement is usually the method that is used to measure the volume of an irregularly shaped object. The object is simply submerged in a liquid and the volume of liquid that is displaced is measured.
As an example imagine a 100 ml graduated cylinder with 50 ml of water in it (half filled). A small statue of a dog is dropped into the cylinder and it is noted that the water level rises to 63 ml. The displacement of the water caused by the dog statue is 13 ml (63 - 50). So, the volume of the statue is 13 ml which is equal to 13 cm^3 (cubic centimeters).
Dissection is also used in the real world for volumes of large irregular objects. Objects of irregular shape are virtually broken down into regular shapes. The regular shape volumes are then calculated and summed to estimate the volume of the irregular shape.
I hope this answers your question.
You would use displacement. That is, measure a volume of water and place the irregular object into the graduate or measured amount. The difference between the two measured volumes becomes the volume of the irregular object.