Coleslaw was most likely brought to the United States by Dutch emigrants well over one hundred years ago. Cabbage had been brought from Europe a hundred years before that. Coleslaw became popular in the early 1900s with the advent of mayonnaise in a jar. Today, coleslaw is one of the most popular salads around and one of the top side dishes of barbecue.
Most traditional coleslaw is not made with mayonnaise but that's the most popular form today. The combination of coleslaw and barbecue goes back a long time. Traditional Carolina style barbecue sandwiches are typically topped with shredded cabbage or coleslaw.
The real secret to coleslaw is to remember that this is basically a cabbage salad (that's actually where the word comes from). You don't want coleslaw that needs to be served in a bowl. Coleslaw shouldn't be a runny mess that soaks through your paper plate. The problem many people have is that they shred the cabbage too fine. Cabbage tends to be pretty low in water, but if you run it through a food processor you're going to get a wet, drippy mess. Cabbage for Coleslaw should be chopped with a sharp knife and kept coarse enough that the water stays in the cabbage. Don't grind your slaw into a soup.
The next point is to only add similarly dry vegetables to your coleslaw. Tomatoes, citrus fruits, avocados, and other mushy, wet vegetables need to stay out. Carrots, onions, celery and similar veggies are great. As for the dressing, remember that it is a dressing and not the primary ingredient of coleslaw. No matter what you mix together to dress your slaw it needs to be used in moderation. This means just enough to coat it and not drown the coleslaw. You can use most anything for your dressing including mayonnaise, vinegar, fruit juices, and oils.
Lastly, you need to season your coleslaw. Traditionally, people tend to use black pepper, salt and some herbs and spices. Caraway seeds, sesame seeds, red pepper flakes (if you want some heat), fennel, garlic, parsley, dill, oregano, and basil are all used in Coleslaw. Remember that you will want plenty of flavors because you don't really want the taste of the cabbage to be all you get.
Once you have chopped the cabbage, the other vegetables, and the dressing ready, all you have to do is mix it together. The thing that makes Cole slaw different from other salads is that you want to mix it all together ahead of time. Coleslaw is best if it has had an hour or two in the refrigerator for the flavors to combine.
Now there are a lot of recipes out there so if you're picky about your coleslaw I'm sure you can find the right recipe for you.