A beaker, flask, or graduated cylinder. You have to put water in the container, record the volume, then place the object in the container and calculate how much the volume of the water raised.
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The water displacement method. The volume of an object is equal to the volume of water it displaces. For small objects, this can be measured by the change in water volume in a graduated cylinder.
Depends on the size of the object. One method (if the object is small) is to first fill a precisely graduated container (showing volume) with liquid that the object does not dissolve or have a chemical reaction and which will submerge in the liquid completely (it must be heavier than the liquid, density-wise). Note the reading of the top of the liquid, that's the volume of liquid alone. Now slowly immerse the object and note the new reading on the graduated container. The difference is the volume of the object.
If you can weigh the object and know its density then V=(M/D) where V is volume, M is mass and D is density.