I’m steaming some screenshots from the Steam Community here, so hopefully they work. In each case look at the yellow box in the top right of the screen and ignore everything else.
See the 6 on the Car Factory and Truck Factory? That means if those factories produce 6 goods they’ll level up. To make them produce goods, give them input resources, and if their output pile is full, take some goods elsewhere. Also note that the factories are level 0 here, as there’s no stars.
Here there’s a red star on the quarry, that means it’s level 0 waiting to go to level 1. It needs 6 dynamite. You can tell this because of the flashing dynamite sybmol and the 6 (top left of the quarry – the big 6 in the bottom right means it’s “size 6”)
It’s a bit hard to see here, but the cannery needs 100 bricks to go from level 2 to 3 I think it’s size 4? Hard to tell in the screenshot. The size 4 shearing shed is already at level 3, and the size 10 clothes storage is already level 3.
Note that: With level 0->1, you usually need to make the factory produce it’s size in goods (which is also, for level 0, the size of it’s input and output piles*). level 2 -> 3 is usually double it’s current storage size. Not sure about level 1 -> 2, somewhere inbetween? 1.5x? There’s probably numbers on this somewhere but I can’t be bothered finding them.
* though in that first screenshot it isn’t, which clearly means I have no idea what I’m talking about. I think it’s some scale factor of the industry size, level, with each level being capped at 10, 250, 500 respectively?