This is a great question because every single one of us, to a man or woman, has/had the same question at some point in our life or will at some point . In my experience private courses / clubs run the gamut from low-key and laid back glorified public courses to high end stuffy / super traditional clubs. The most basic thing I can say is once it’s balls in the air it’s just a bunch of grass, sand and water, no different to any other golf course, apart perhaps from conditioning and possibly layout (although there are certainly many public courses that can eat the lunch of many private courses layout / architecture wise). So it’s just golf, have fun, don’t be an a-hole, use the etiquette you’ve already been playing with and it’s hard to get into trouble.
Many people have already commented on the details but I’ll reiterate:
Usually bad form to change shoes in parking lot. Wear some “nice” shoes (aka not tennis shoes) and bring your cleats in a little duffel bag and change them in the locker room. If you don’t know where the locker room is just ask the first club employee you see. If nobody is in the locker room when you get there, just sort of stand there and wait or poke around and there should be an attendant somewhere who will be more than happy to help you. Just tell them the name of the member you’re playing with and they’ll hook you up with your own locker. Tipping these guys is never a bad idea, 5 bucks is fine I’d say but others may think that’s light or heavy, dunno.
Many of the nicer clubs have a no hats policy inside parts of the clubhouse. I always err on the side of caution if I’m not sure or just observe and follow the lead of others.
If the club has caddies, and I don’t know standard operating procedure around tips, I’ll ask my host walking up 17 or 18 if I can help or take care of the tips. In 100% of my experience the host has always shook his head and thanked me for the offer and then taken care of the tips for our group once we’re off 18 green. Just in case a host hits your bid on that offer I always bring a few hundo in cash but have always left with it apart from the many times I’ve lost it on the course.
I send a thank you e-mail to my host after the round. If it’s a really good relationship or a particularly baller track (I’m talking on the top 100 you can play list, or not but still super exclusive), I’ll even send a bottle of vino and a handwritten note but that is certainly not normal/required. E-mail or text thank you is required in my view.
About all of the above, not necessarily universal so I would just ask host ahead of time if there is anything special I should know. Don’t have to but if you’re worried about it they’ll be happy to answer the question and it’s one they’ve gotten many times before.
But back to basics, it’s just golf. Just be a nice person for 4-5 hours, follow a little bit of tradition if it’s called for, and voila you’ll get an invite back which is one of the main goals in all of this.