Don't think it really changes from one kind of pot to another.
Probably easier to take care of than cheap pots which could be damaged easily.
Keep them cleaned as soon as possible after using (in other words don't leave them til the morning to wash!)
Dry after washing. Especially type that would have a tendency to rust! Those should be wiped down with your oil right after drying and befor e putting away.
Keep an eye on pans that need to be seasoned. I find it pretty obvious when it needs care and I think, once you have some, you will too. There are many suggestions on how to do it, both here and on the 'net. All pretty much the same.
I also like to dry them as I dislike water spots, on glass and/or shiny pans.
I'm sure you will now be inundated with tons of advice.