Be on time.
Learn a few words of French. It’s amazing how many people actually speak some English once you’ve initiated the conversation in their language.
Hold the glass by the stem, and don’t break it!
Spit. Seriously. Follow the lead as to how and where, if not, ask before your mouth is full. Only drink the sample from the last couple of bottles/barrels, usually with the quip “there’s no way I’m spitting that”.
Same for the leftovers. It rarely goes down the drain in Burgundy, usually either all mixed in a jar, or straight back into the barrel (some people prefer to do it themselves rather than let you do it, if you’re not comfortable with doing it just pour it back into the person’s glass).
I don’t think gifts are mandatory, but if you do bring something that is not widely available in Burgundy (or wherever you’re tasting). Also contrary to popular belief I’ve observed that a lot of owners have varied tastes and the cellar to match. So my experience directly contradicts Stuart’s here: at most of the top domaines I have visited the owners (and often employees) are winelovers and have a huge network of friends and acquaintances in other regions. A lot of them learned their trade in Alsace, the Rhône or Italy…
Do your homework. Have at least a vague idea of who you’re visiting, what they’re doing, what’s usual for the area (so yeah asking about the grape variety isn’t such a good idea, unless you like to be the butt of their next joke).
Re: questions, either ask pertinent questions about what they’re doing specifically (if you have the knowledge, e.g. comparing terroirs or winemaking techniques), or branch out to something else entirely (food and restaurants tend to be a great topic). Share an anecdote of some great time you’ve had with one of their bottles.
If you want to buy a few bottles, ask nicely, directly, and roll with the answer.