Just to be clear, I'm not talking about adding oil, just about distributing the oils that naturally come out of the brewed tea. You can see this especially strongly if you brew Chaozhou gong fu style with a ton of leaf, and even some crushed leaf... the tea oils will be very thick and shiny on the pot, and if you don't even them out, you'll see shiny streaks on the pot, or around the button.
So I just use a wet or damp cloth to even things out... I think the best is to leave things as they are during the session and use the cloth / brush at the end, so that the stains have time to build up, but because I'm fidgety, I have to admit to sometimes polishing a little during my tea brewing as well. I have heard it's not a good idea to polish too much, and polishing with a dry cloth might not be good either.
See also the comments (including some questions from yours truly) on Tim's web log:
http://themandarinstea.blogspot.com/200 … xings.html
esp. the comment from Tim:
Over polishing is a no no to me, collectors call it "Monk Head Glow" which is a more artificial shine then a glow representing jade -"Treasure Glow".
I don't do anything to the inside of the pot; rinse once or twice with hot or boiling water, let it dry for a while upside-down, and then dry rightside-up with the lid off for 2-3 days.
I also don't do any special pre-seasoning... just some hot / cold water through the pot, gently scrub off any obvious stuff inside that shouldn't be there, and make tea in the pot. If it's a used pot and I don't like how it's seasoned, I might boil it for a little.
Personally, I don't think polishing or not will affect the brewing characteristics of the pot. However, if you actually polished the pot with oil or wax, I imagine that could potentially affect the famous "double porosity" of Yixing clay, and might also repel water.... this would probably not be a good idea. I guess if you had too much of a buildup of tea oils, it could have the same effects, but you don't really ever hear people talking about that, so I don't know. Personally, I don't believe in using anything other than tea and water on the pot.
There is talk, of course, that with seasoning, the inside of the pot will take on characteristics of a particular tea. But this could take a very long time, and I don't know if it'll ever get to the point where you can brew tea in the pot without using any tea leaves at all, like in the old legend.
I do have some pots that are of an especially porous clay, and I can sometimes smell the last tea I brewed in them for several days, or even longer.