I clean breechplug, barrel and frame after every session. This includes removing the barrel from the frame. I clean the barrel using the plunger method, basically plunging hot, soapy water through the barrel. Gets it very, very clean. I leave the barrel and breech plug to dry for several hours to overnight. I then wipe everything down with gun oil and reassemble the gun. Muzzle-loaders.com has these pipe cleaner's that have nylon stud embedded and those do a great job cleaning the plug.
With my CVA I would also remove the firing pin and clean that and the spring after every session. My T/C doesn't get nearly as dirty so I won't be doing that until the end of my last hunt.
At the Range, I keep a zip lock bag with patches that are saturated in windex and I run one of those plus two dry patches after each shot. Before shooting, I run two dry patches and then pop 4 primers to foul the barrel.