I shoot flint with straight black powder, and hot water + a little dish soap always works for me. Push the ramrod w/soaking wet patch in and out like a plunger. With a caplock, you can fit a plastic or rubber tube over the nipple (other end in a can) to keep the dirty water from spraying all over. With a flintlock, wrap a towel around the stock to help keep the dirty water off the stock and point the touch hole down. Some rifles allow you to easily take the barrell off the stock, which can make things even easier.
Follow with a couple clean wet patches just to be sure. Follow with dry patches until dry. Follow with light oil. The hotter the water, the better since the bore dries quicker. Cleaning's not complicated, but it can be messy. I don't shoot Pydodex, and I don't know it would any different, but several folks make cleaners specific for Pyrodex.
Check around your local gun club or range for somebody who shoots muzzleloaders regular. They should be able to give you advice on the care and feeding of a ML, as well as advice on what type you might like to buy.