Some initial handwaving of mechanics to use as a basis:
We'll assume that the material in question can react with a limited range of other materials, and undergoes an excessive density change during its phase change from a liquid to a solid. Kind of like how liquid water has a density change when it freezes and turns to a solid, but we're upping this mechanic by several orders of magnitude. This allows it to cycle through the environment kind of like water, and doesn't just end up forming the upper atmosphere.
We'll really want that "limited range of other materials" mentioned earlier, simply to handwave what that kind of matter might do to living plant life... Complex life forms might struggle to evolve on a planet where getting rained on might cause parts of them to balloon in volume at random and float away.
- Probably safe to assume that forms of carbon common in life disrupt the reaction in some manner, otherwise life is going to be really awkward if this stuff isn't super super rare: And where would the fun be if it wasn't at least somewhat common?
The density of air being about 1.225Kg/m^3 should actually help us keep much of the worst case scenarios to a minimum, because "Full on Floating bits" are probably unlikely to manage to stay in single massive chunks for long after getting slammed into trees and against exposed rocks. Anything really big that does manage to gather will stand a high chance of cracking into smaller bits, so our towns and cities probably don't have to worry about having whole mountains blunder into them on a regular basis.
Having the material expansion based on phase change from a liquid to a solid will also aid in limiting the size of chunks: As float-rain hits material it can react with, it will start expanding on the top of the material, eventually breaking the expanded low-density stuff off from the material below. This will cause floatstone based erosion to mostly flake off in layers, or more likely sort of corn kernel or mushroom shapes as reaction regions try to expand in all directions, but will take the path of least resistance: Up and out.
Temperature limitations on the reaction will also help keep things 'interesting'. Such as a minimum temperature and endothermic reaction would help more material saturate and bind with the float-rain before reacting to become full on floatstone. Larger chunks could stay together longer before 'lift-off', and the liquid could reach deeper into the ground before the reaction begins.
Locals may be terrified of "very hot summers" as it means lots of land suddenly erupting at random and fresh floatstone nodules hit their thermal tripping point and expand... but the endothermic nature of said reaction would naturally put a brake on too much going too far in a very short time.
Having it slowly break down in sunlight, shedding more of its 'non-floaty-mass' in dust like volumes would mostly keep boulders from falling out of the sky, and also give it a mechanic for returning back to float-rain/vapour status: It sticks to clumps of non-float-matter, or forms with pockets of it inside, but is naturally far less dense than air: Once enough mass is shed it shifts to higher in the atmosphere, where it breaks down the rest of the way and phase changes back to liquid when it runs out of 'reaction matter' to hang on to.
But all this brings us back around to the important part of the question:
So how would we best want to deal with low density floating stones?
- Deflection is likely our best bet.
Successful settlements are probably going to be on the leeward side of hills, and hiding in holes during hurricanes is highly advised.
- Long, low sloping rooflines, such that blown floatstone is likely to roll up and over buildings, sounds like a good idea.
- Large vertical glass windows are probably not going to be popular.