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For the Dressing: Whisk together vinegar, sugar, oil, garlic, black pepper, and celery seeds in small bowl.
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For the Slaw: Combine cabbage, carrot, and onion in a large bowl. Sprinkle with sugar and salt and toss to combine. Let stand five minutes, then transfer to a large colander and rinse thoroughly under cold running water.
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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.
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Pour dressing over vegetables and toss to coat. Adjust seasoning to taste with salt, pepper, and/or sugar.