During a major kitchen remodel that includes removing structural walls and pouring new foundation piers and extending the house, along with the typical re-plumbing and electrical work, how often should the client (me) be walking through the job site and talking to the general contractor? Should I ever be talking to the subcontractors, apart from being nice, or does everything go through the general contractor? What do contractors, and subcontractors, want from the client?
I'd be walking the site daily. This isn't a new building with major safety hazards. It's your home, and you should have free access outside work hours. Any hazards should be eliminated, marked, or secured by then.
I'd want to feel comfortable raising issues with the GC at his/her convenience. I'd recognize that my project is not their only one, and that they have limited attention split among several (or many) clients. Call or email and wait for a reply.
I would not address subcontractors directly other than sharing greetings in passing (while staying out of the way). That would be a violation of unwritten (or possibly written) protocol. You're paying your GC to do the negotiation and communication with the subs, and you'll cloud the water if you get in between. Also, as stated earlier, you shouldn't be on the job when they are.
My $.02, however biased it may be for having been both a GC and a sub as well as a customer at various times in life.
Keep your crap out of the way. Few things frustrate a contractor more than having to work in confined spaces for no reason other than lack of consideration on the part of the customer.
Be courteous. The people working on your home will find it easy to not care about their level of quality if you give them reason. Conversely, treating them with respect is likely to earn extra care.
If you like, offer a cold drink or cookies or something now and then. This extends the being courteous thing to something approaching bribery, but really it just generates mutual good will. This is important when you're paying a pile of money for something you have to live with daily.