Great question.
"Working in", "working for", and "working at" are used interchangeably in most cases.
Ex: I work {in/for/at} a bank. (They all mean that I am employed by the bank.)
However it is important to remember that prepositions are native-speaker knowledge-governed. Not everyone who speaks the same dialect (national or regional) uses the same preposition as everyone else. Sometimes one has to use the preposition that makes most sense (if something's sitting on top of the table, one must say on the table, not by the table or under the table), and sometimes not (Let's walk {up/down} this block for a few minutes , regardless of whether the block goes uphill or downhill or the numbers ascend from 0 to 100 or descend from 100 to zero).
Context is very important, and idiomatic usage for one's regional or national dialect is also important.
As a guide, you "work for" an employer, "work in" a department, "work at "a location.
Ex: I work for Apple, in the finance department, at the San Francisco Office.
It can get a little confusing though, because there is a lot of overlap. An employer name can be used to point to both the employer and the premises, at least locally where everybody knows the name.
Ex; I work for/at Apple. (The would both work).
Similarly, where a business has only one function, the employer and the 'department' overlap.
Ex: I work for/in a restaurant.
This is why you have never heard "She works for a shoe factory" but you have heard "She works for a law firm." 'Law firm' can refer to both the employer and the premises ("There's a law firm on the 4th floor"), but 'shoe factory' refers only to the premises.
