In evolutionary terms, claws like those of cats have evolved to be grappling hooks, to provide an advantage when capturing prey or when climbing. They are actually not particularly well evolved to be weapons designed to produce injury in animals of similar size.
Consider that their primary use is to capture prey, they have sharp points, but no edges, so that once the point has lodged in the victim, if the victim pulls against the claw, that will not result in a cut which allows the victim to slip free despite the injury. Cats grapple and climb with their claws, and kill with their teeth, and any use of their claws as a weapon is secondary - consider that cats use their claws against each other in fights, and while they do produce injuries, they are seldom lethal or even particularly injurious.
Animals with truly lethal weaponry seldom use that weaponry against others of their own species. Consider that some species of snake are venomous, but they rarely use their venomous bite against other members of their own species, instead settling their rivalries by wrestling.
So, cat-like claws are not a particularly good weapon in themselves.
However, there are potentially other types of claw. A particularly large claw might be used to inflict a fatal injury by penetrating the body of a victim deeply enough to cause a fatal loss of blood. It was thought for some time that dromaeosaurs such as Deinonychus or Utahraptor might use their huge toe claws to inflict fatal injuries, but the morphology of the claws and the anatomy of the limbs to which they are attached suggest that the claws are held elevated while running to help them retain their sharp point, and that they, too, are employed as grapples, to allow the predators to climb a much larger prey animal.
Still, the potential for the application is sound. A large claw with a sharp point, a broad base and serrated edges might be used in repeated stabs from relatively short, thick digits on a long fore or hind limb. Such a weapon would be used with the predator approaching the prey and then quickly and repeatedly stabbing with its dagger-like claws, hoping to inflict sufficient injuries to cause a rapid loss of blood.
The other type of claw is much like the claw of a cat or a raptorial bird, save that its inner curve is sharp, and injuries are inflicted on prey by first grappling, but then continuing to apply force to the grip, the sharp inner edges of the claw being pulled through the victim's flesh causing deep, severe injuries. The objective here is again not primarily to grapple, but to cause blood loss, however such claws would allow a small predator to effectively climb a large prey animal while at the same time inflicting large, ragged, profusely bleeding wounds.
A claw-like weapon that is used to inflict injury rather than to grapple is exemplified by African Leopard Claw knives. These have a sharp edge, and not just a sharp point, and while these weapons were intended to cause injuries similar to those caused by the attack of a leopard, the fact that the inner edges are sharp would cause significant differences in the wound that a trained investigator or someone with experience in the injuries cats inflict on their victims wouldn't mistake for the injuries inflicted by a real big cat. These are used in a slashing manner, but the cutting claws I describe above would be used in a grapple and squeeze/slice fashion.
So, to move on from my extensive digression into zoology, if we had a clawed cat-person, the claws would likely be most effectively used as grapples. She could grab an enemy - even with one hand - and it would be near impossible for her target to pull away without employing a motion that does not work in opposition to the claws, but instead applies a force to the side of the claws, threatening the integrity of the joints of her hands. This would not be particularly easy for a grappled opponent to do.
Once the cat-person had grappled her foe, she could then employ whatever other weapons she had, either natural or artificial. She might have sharp teeth that could inflict a fatal bite, or, more reasonably (since getting her head that close to an opponent, who may well be human or humanoid and potentially armed, may not be the best idea), she might grapple with one hand (preferably immobilizing the opponent's limb and reducing the opponent's potential for attack or defense) and then use an artificial weapon such as a dagger to inflict more serious injury with the other hand.
TL;DR: Grapple the opponent's most favored attacking limb with the claws to immobilize the limb, and attack for effect with a real weapon.