I analyzed the associated section from the GameConfig.xml according to some information that was provided here.
<!-- ============= DUNGEON ROOM COUNT ============= -->
<DungeonRoomCountMin>
<CurveOperation Type="Multiplication">
<Curve Abscissa="Level">
<CurvePoint X="1" Y="12" Link="true" />
<CurvePoint X="8" Y="26" Link="true" />
<CurvePoint X="11" Y="28" Factor="0" />
</Curve>
<Curve Abscissa="PlayerCount" BaseValue="1">
</Curve>
</CurveOperation>
</DungeonRoomCountMin>
<DungeonRoomCountMax>
<CurveOperation Type="Multiplication">
<Curve Abscissa="Level">
<CurvePoint X="1" Y="16" Link="true" />
<CurvePoint X="9" Y="32" Link="true" />
<CurvePoint X="12" Y="34" Factor="0" />
</Curve>
<Curve Abscissa="PlayerCount" BaseValue="1">
</Curve>
</CurveOperation>
</DungeonRoomCountMax>
I entered the given values (in bold) into a table and extrapolated the missing values. Link="true" means that linear interpolation between two successive values is used. Factor="0" sets the slope to 0, so following values stay the same.
The total amount of a resource generated gets divided between players, rounded up.
Complicating things is the fact that the initial resource yields are not uniform (on an Easy difficulty it's 5 industry, 2 science, 4 food), and the true yield is not displayed anywhere.
Due to this rounding, it is possible to not see any effect from an upgrade, or to maximize your benefit by crossing the "threshold" and squeezing an extra +1 from the system.
In a 3-player game the starting 5 industry per door gets divided 3-ways and rounded up to 2 per player. Starting 2 science is similarly divided into 3 shares and rounded up to 1, while starting 4 food is divided and rounded up to 2.
In such a game, building a first tier generator which adds 3 resources per door opened will give every player +1. Building a single second tier generator produces no improvement over the first tier ones: the total yields would become 5+4=9 for Industry, 2+4=6 for Science and 4+4=8 for Food. However, constructing a second second tier Industry or Science would give each player an effective +2 to the corresponding resource, while a second second tier Food generator would only give +1.
Mechanical pals, multiple generators and Operating further complicate the picture, but the calculations seem to hold: find the actual (hidden) yield, divide, round up or down. This is a chore, but can save one from wasting resources on a useless mechanical pal. And in a roguelike, every last drop counts.
Best Answer
You have very little control over it, it's mostly the RNG.
You can get it from...
Every time you open a door there's a chance of dust dropping, which is a random amount, I think I've seen numbers from 2 to 9. The hero Max has a skill which raises the amount gained if he is the one to open the door when dust is found in a room, he gets this at level 5 according to the wiki, and it's also available on the "third eye" item.
I believe every time you kill a monsters there's a chance they'll drop one dust, however it might be more complicated than that. The heros Golgy and Sara have a skill which increases the likely hood of dust dropping from monsters, it looks like it only applies to monsters they kill, they get it at level 3 and 7 according to the wiki.
Some merchants use dust as currency to buy and sell. If you have items you don't need, and don't expect to need, you could sell them for dust.
There's a Major Module called the Shop which allows you to store a Merchant, which can build Dust if it's operated while there's a Merchant in it.
There's at least one event/tower thing where you can pay industry for the possibility of dust.
Note that dust is reset after each level, as are certain excess items, while industry is persistent, (but more dust might let you get more industry, or food, or science) which effects whether or when selling items or spending industry is worth it.
As I said, I haven't played the release version much yet, there's likely to be more specific items and modules, but that's everything I'm aware of.
Regarding tactics/strategy, it's more about adapting your controlled area/which doors you open/build things on to make use of the dust that you have, as opposed to taking specific actions that grant you more dust, since often those actions simply aren't available.