I think this is a really difficult thing to get right. On the one hand you want to be friendly and chatty, and on the other you want to remain professional which means you dont want to appear nosey, rude or come across as a gossip.
I let the client lead the way. My lead question (for nails) is "so are you having these done for a special occasion or did you just fancy a treat?". Your client will then give you a lead, and you can discuss their special occasion, birthday, wedding etc, or you can just talk about how its nice to treat ourselves for no reason, we deserve it, we work hard etc, what do you do for a living incidentally? and so it goes!! I dont ask questions about their personal life such as spouse or children unless they offer the information freely.
Sometimes it becomes clear that the client doesnt want to talk, and that's fine theres nothing wrong with letting them sit and relax in silence. Lots of techs feel the need to fill the silence, but really when its clear that the client doesnt want to talk the best thing to do is get your head down and get on with the job. You will have reasons to communicate with the client throughout the service to check their preferences or how they want something to look, so there's still opportunity to show the client that you are open, friendly and accommodating; a lack of chit chat doesnt have to mean you are being hostile.
At the other end of the scale you have the clients who want you to do their nails and provide a therapy session at the same time, and some clients do share some very personal, sensitive, even intimate information! I think you have to tread very carefully here, it is vital that you dont get a reputation for gossiping. In this situation the thing to do is smile, laugh in the right places etc, but dont say anything to fuel the conversation, especially if the client is talking about someone other than herself. Dont be ignorant, but dont join in the conversation either.
Finally there's my golden rule. I never discuss a client with another person for any reason, and I absolutely would never discuss a client with another client, not even to say "oh, so and so was in for her nails the other day", as you've no idea what problems you might be causing. Also, I never discuss another salons treatments or practices. You will get clients coming to you saying they used to go to xyz salon but they were rubbish, and even if you agree with the client, dont involve yourself with the conversation, nothing makes you look less professional than slating another salon or therapist.