1) Service: It's not a normal restaurant. Don't expect to have the same standard of service. If you need water and everybody is busy, feel free to get your own. If you drop your napkin, I suggest you pick it up yourself. Under no circumstances snap your fingers at the wait staff, they aren't your servants, they are probably friends or related to the host. The hostess may even have given birth to them.
Keep your cutlery between courses, French style. The less washing up, the better.
2) Drink: Bring your own booze. Most supper clubs don't have an alcohol license. This is great for you as a guest: take the opportunity to pay what you'd normally spend in a conventional restaurant on the cheapest bottle of wine on the list (£10 to £15) on a very good bottle of wine with no mark up. Soft drinks: most supper club hosts do not have a large fridge containing a selection of soft drinks complete with price list, so if you have a soft drink you particularly like, do bring it along. Supper clubs tend to offer tap water rather than mineral water, so again, bring your own if you prefer that. Some, admittedly few, supper clubs charge a corkage fee for wine to cover provision of glasses. (This may sound unfair but providing wine and water glasses for each guest and washing them up is one of the most costly and time consuming aspects of a supper club, especially when they don't earn money for drink.)
Do bring your own drink. I've had occasions where people didn't bring their own and helped themselves or expected others to share their wine with them. More often this is fine, but can sometimes lead to irritation and people hiding their bottles under the table. At the same time, do be generous, do share with your table. If it's white wine or champagne, bring it ready chilled.The host/ess probably won't have room in his/her fridge.