Besides the difference in dressing, both types of coleslaw are pretty similar. It involves shredded cabbage, and often some other veggies. Shredding cabbages is pretty simple to do with a good, sharp chef's knife. Quarter the head, leaving the core in place. Start from the top edge, diagonally away from the core. Slice down through the quartered head, thinly, working your way toward the core. The first couple of times, you won't get really thin shreds. But, a little practice and you'll find that it gets better.
Or, joining the 21st century, run it though the shredding disc of your food processor. Personally, I'm too lazy to haul it out of the cupboard and then do the extra dishes. So I've gotten lots of practice with my knife.
Other veggies that work in coleslaw include sweet peppers. Not just bell peppers, but try a cubanelle or sweet banana pepper and try that with a vinegar-y dressing. Cabbage and peppers appear together in your CSA boxes in the fall. The zip really makes it interesting. Other options include carrots, cucumber, fennel, your Vidalia onions if you have any left, scallions, shallots, avocado (especially yummy in a creamy dressing)... Just remember to either grate or very thinly slice all of it.
You then create a dressing, toss your veggies in it, and (this is very important) let it sit in the fridge overnight. Slaw is pretty much always better after the goodies marinate for a while. Stirring in some other additional bits of a different texture really makes it interesting, too. Try toasted pine nuts, raisins or dried cranberries, sesame seeds, or the like.
As for that dressing, there are some pre-made options, such as Marzetti or Green Goddess dressings. A little Miracle Whip and some lemon juice works great too. For those on the vinegar-y side, use some sort of vinegar (obviously) like white, cider, malt, white balsamic, or even a more creative acid like lime juice. Add some salt and some sweetener (sugar or honey) and it's dressing. Spices work well in either. As in our previous discussion on spice palettes, pick a region and use complimentary ones.
And that's how you ad lib coleslaw. If you'd rather work from a recipe or read some for inspiration, this is my go-to one (the pickled one), but the other ones at the same link are good too. This one is more creamy, using avocados and tomatillos to make a slaw for salmon tacos -- which are really fantastic. This one has a vinegar dressing with dijon mustard. And, as soon as we get fennel in the store, this one is my next one to try. (link requires a subscription to Cooks Illustrated)