Combine oil, onion, garlic, and 1/4 teaspoon salt in a large saute pan; cook over medium heat, stirring occasionally, until onion is lightly browned, about 5 minutes. Reduce heat to medium-low; cook until onion is soft, about 10 minutes.
Add vinegar to pan, and raise heat to medium-high. Add kale, 1/4 cup water, and remaining 1/2 teaspoon salt; cook, stirring, until kale begins to soften, about 3 minutes. As the pan becomes dry, add another 1/4 cup water, and cook until the kale is tender, about 3 minutes more. Serve immediately.