Definitely completely porous is straightforward: Archimedes Principle will do that: weigh it, then immerse it in liquid and measure the volume change.

Where it's hard is semi-porous or mixed materials. Closed cell foam is an example of this - it's made of two very different materials, the plastic that makes up the foam, and the gas that makes up the voids. You can't non-destructively measure the density of the two parts together. The brutal approach is generally used - crush it to burst all the bubbles, then measure the density of the resulting lump.

This matters, because often porous materials contain trapped gas. So you measure the density as above and get quite different results from different samples. Think of immersing a sponge, then squeezing it - if bubbles of air come out you would have measured different densities before and after. How do you know that you have no closed cells containing gas? Answer: you crush it then measure it.