Density is mass per unit volume, so when measuring density, you find the mass of the object and divide it by its measured volume. All measurements include some uncertainty, however, and certain kinds of errors can increase the uncertainty in your calculation further still. Always try to use the most accurate tools available to reduce errors when measuring density.
There are many different instruments you can use to measure liquid volume -- kitchen measuring cups, beakers, graduated cylinders and volumetric pipettes are a few examples. Unfortunately, not all of these instruments offer the same level of precision and accuracy. Beakers and kitchen measuring cups are the least accurate of these devices. Graduated cylinders are somewhat more accurate, and volumetric pipettes are the most precise of these tools. Depending on what kind of instrument you use, then, your measurement of volume may have an increased level of error or uncertainty -- in other words, if you use a beaker to measure volume, your measurement could potentially be much further off from the true value than if you used a volumetric pipettes.
Regular Solid Volume
If a solid has a regular shape like a cube or a cylinder, its volume is easy to calculate using simple geometrical formulas. You will still need to measure its length, radius and so forth, however. So the ruler you use to take measurements introduces a possible source of error, since your measurement will only be as accurate as your measuring device. Moreover, if the shape of the solid has some irregularities -- a dent in the top of the cube -- your calculation of its volume will be off by the amount of the irregularities.
Irregular Solid Volume
If a solid is irregular in shape -- a wood chip, for example -- you would need to use calculus to calculate its volume, and the calculation could become very difficult, depending on the shape of the object. In this case, you would be better off determining the volume by submerging the object in liquid and checking to see by how much the volume changes. You must choose a liquid in which the object sinks rather than floats, however, and it's also important to make sure the object does not soak up the liquid. If you were to use wood chips in water, for example, they would float and soak up some of the water, skewing your volume measurement.
Density varies with temperature. Over the range of temperatures that people encounter in everyday life, this variation is negligible for many kinds of substances. It introduces another possible source of error, however, because if you measure density at one temperature, your result may not be valid at another. Moreover, the density of a gas varies widely with pressure and temperature, so for a gas your result is only meaningful under specified conditions.
Mass and Other Considerations
The final possible source of error is your measurement of mass. Typically, mass is measured using a scale or balance. The accuracy of your measurement will depend on the kind of scale you use. A kitchen scale, for example, is probably less accurate than a calibrated scale in a chemistry lab. Generally, scientists will take these possible sources of error into account when they make a measurement by reporting an uncertainty value. In other words, rather than reporting density as just "x," they will report it as "x +/- y." The greater the uncertainty, the greater "y" will be, so this uncertainty value gives you a sense for the reliability of the measurement.