You always need a mass (on a balance, zeroed first) and a volume.

• Regular solid: measure the length, width and height with a ruler or callipers and multiply.
• Irregular solid: lower it on a thread into a measuring cylinder of water. The rise in level is its volume. For a big object, use a eureka can and catch the water that overflows.
• Liquid: weigh an empty measuring cylinder, add a known volume of liquid, weigh again. The difference is the mass of the liquid.

volume of object = volume after − volume before

• Read the measuring cylinder at eye level, from the bottom of the meniscus (no parallax error).
• Lower objects gently so water does not splash out.
• Choose a measuring cylinder the object fits in with the smallest scale divisions you can.
• Repeat, spot anomalies (results far from the rest), leave them out and take a mean.

uncertainty ≈ ± half the range of the repeats

Variables: the independent variable is the object or liquid you test, the dependent variable is its density, and the control variables include the water temperature and the balance you use.