In general, a W-2 employee pays income tax in the state where they actually physically live and perform the work, even if the business is headquartered someplace else. (The state of their domicile, or permanent residence.) If an employee lives in state A and works temporarily in state B, they file a non-resident return in state B that reports their state B income, and a resident return in state A that reports all their world-wide income. State A will usually give a credit for taxes paid in state B to reduce the impact of double-taxation.
Sometimes, an employee who lives and works long enough in state B will be deemed a statutory resident, even though they are not a domiciliary resident. That makes things more complicated.
A few states have a "convenience of the employer" rule, meaning that some times, an employee who lives and works in state A for an employer located in state C can be required to pay state C income tax.
https://smartasset.com/taxes/convenience-of-the-employer-rule
I don't know what you mean by cheat sheet, you pay state income tax based on the laws of the state or states where your permanent residence is located, and the state where you lived and performed the work, if they are different.
I have no idea what state laws are regarding the business' requirement to pay state unemployment tax, when the business is located in state C but the employee lives and works in state A or B. You would have to check the laws of those states.
