Start by finely chopping the cabbage and carrots. A sharp knife will make this task much easier.
In a large mixing bowl, combine the chopped cabbage, carrots, and white onion. Toss them gently to ensure an even distribution of ingredients.
In a separate bowl, whisk together the mayonnaise, white distilled vinegar, sugar, salt (or celery salt), and celery seed until smooth.
Pour the dressing over the vegetable mixture. Using a spatula or large spoon, gently fold the dressing into the cabbage and carrots.
Cover the bowl with plastic wrap or a lid and refrigerate for at least one hour to allow the flavors to meld.
Give the coleslaw a good stir before serving. Enjoy it as a side dish or on its own!