There is no spell attack associated with hex. You cast it on the target and it affects the target until you stop concentrating or until the duration ends.
Hex doesn't cause any direct damage to the target; it adds an additional 1d6 to other attacks you make against the target. If the target dies you can move hex to a new target.
Note that this is different than most spells that don't require a spell attack roll, in that it always succeeds. For hex, there is no save to resist the spell or diminish the effect as there is for other non-spell attack spells which have negative effects for the target(s).
This spell is similar to the ranger spell hunter's mark, which has the same behavior.