For the Dressing: In a small bowl, whisk together vinegar, sugar, oil, garlic, salt, black pepper, and celery seeds until sugar is dissolved.
For the Slaw: Combine cabbage, carrots, and onion in a large bowl. Sprinkle with sugar and salt and toss to combine. Let stand 5 minutes, then transfer to a large colander and rinse thoroughly under cold running water.
Transfer vegetables to a salad spinner and spin dry. Alternatively, transfer to a large rimmed baking sheet lined with a triple layer of paper towels or a clean kitchen towel and blot mixture dry with more towels. Return to large bowl.
Pour dressing over vegetables and toss to coat. Adjust seasoning to taste with salt and sugar.
