Path to the Grave only requires a use of your Channel Divinity feature
The Death Cleric's Path to the Grave feature states:
Starting at 2nd level, you can use your Channel Divinity to mark another creature's life force for termination.
Channel Divinity is a feature every Cleric gets, and it states:
At 2nd level, you gain the ability to channel divine energy directly from your deity, using that energy to fuel magical effects. You start with two such effects: Turn Undead and an effect determined by your domain...
When you use your Channel Divinity, you choose which effect to create. You must then finish a short or long rest to use your Channel Divinity again...
Beginning at 6th level, you can use your Channel Divinity twice between rests, and beginning at 18th level, you can use it three times between rests. When you finish a short or long rest, you regain your expended uses.
At level 2, this feature can be used once per short or long rest; both Turn Undead and Path to the Grave count as a use of Channel Divinity. Thus you can use either Path to the Grave or Turn Undead and then you must complete a short or long rest before you can use either again.
At later levels you get more uses of Channel Divinity between rests.
Notably Channel Divinity does not have any other requirements such as components, reagents, spell slots, or the like. You are only limited by your remaining uses.
The Path to the Grave features goes on to state:
[...] As an action, you choose one creature you can see within 30 feet of you, cursing it until the end of your next turn. The next time you or an ally of yours hits the cursed creature with an attack, the creature has vulnerability to all of that attack's damage, and then the curse ends.
So what happens is you use your action, expending of use of Channel Divinity to activate Path to the Grave. You select a creature within 30 feet, and the effects of the curse apply; the first attack made by yourself an ally that hits the cursed creature will deal doubled damage, though only if the hit occurs before the end of your next turn.
Path to the Grave does not add on any new requirements in its description (Some Channel Divinities do, such as Turn Undead which says you "present your holy symbol"; the ramifications and requirements of that phrase are up your GM). With no additional requirements, Path to the Grave, just has the usual requirements of Channel Divinity, which is none; It only costs one use of your Channel Divinity feature.