How does state residency work exactly?

Although there can be some esoteric legal consequences which depend on which state is your legal residence (e.g. where you can sue and be sued, the government programs for which you might be eligible, tuition at a state school, etc.) for most people the main difference between being a domiciliary of one state or another has to do with taxes.  I don't know where the taxes would be lower for you, in Montana or California. I'm not sure what you mean about "declaring" your state of residence, unless you mean so stating on your tax return, or in applying for some sort of government program.  There's no formal ritual or paperwork which you would need to file.  Moreover, what you "declare" about your residency is not as important as the facts.  If you live in California 9 months out of the year, you will probably be considered a California resident, regardless of whether you have "declared" that you are a Montana resident.