Well, OK, now I have to come through with an explanation. :-)
I use the Pickl-It system, which is a bit pricy, but works really well. I'm sure the alternates would work just as well, but some of them aren't as good of quality.
Cauliflower and carrot is simple...
wash everything... break the florets into small pieces... slice the carrots into thin pieces about 5mm thick (I use a food processor for this!)... stuff the whole mixture into the jar, adding some bulk pickling spices and a few cloves of garlic.... add brine (per recommendations here
http://www.pickl-it.com/blog/636/brine-recommendations/) and put it aside at ~20-21C for four or five days... refrigerate.... eat... :-)