Not all types of interest are suited to all types of encounters. I think Dale Carnegie has a great blanket rule, and most folks can improve their relationships by taking it to heart, but it's something where the same techniques can be applied generically to any situation.
Particularly with bosses/subordinate relationships, I think you're right to be a bit cautious and aware that the line between interested and supportive boss and creepy interrogator is a boundary that is best avoided. Here's some tips that work for me.
Personal Questions - Limited and Open Ended
Particularly in the beginning, keep it light and as open and judgement free as possible. As a person with a non-standard home life, I particularly appreciate questions that don't involve a need to address particular details, for example, good questions include:
- How was your weekend?
- How's it going? ( Particularly great for all times in the day - and I can talk about work or personal stuff - my choice)
- Any fun plans coming up?
- How is the (thing you mentioned before)?
Stuff that's worth avoiding until a detail has been shared willingingly include:
- How's your family? (if we've been estranged for 10 years.... this will be awkward)
- Any assumptions about family connections - even when there's obvious clues (pictures, a wedding ring, etc)
- Assumptions about religion - granted, in the US, it's pretty standard to ask in December "what are your plans for the holidays?" - since even the folks who don't have a religious connection to the season are hopefully enjoying a point in the year where the pace slows a bit.
- Is that (thing you mentioned) finally fixed/finished/disposed of/etc? - there's an implication (possibly unintended) that it should be complete by now.
Stay Positive & Respect Privacy
In my experience, it's not always about asking questions, but about being open when the information starts to flow. For example "Hey, great poster/painting/picture/art/toy/desk gizmo" - is pretty safe (no touching! - don't play with other's toys unless invited) - hopefully they wouldn't display it in public if they weren't willing to own up to having it.
I've gotten quite far in getting to know folks that work for me by being rigorously open to whatever comes my way - the first time a person comes to my office full of tension I know I've got to be as un-judgemental as possible. While I can't say "yes" to everything, being willing to admit that the person is entitled to their desires is very important. It's a good time for things like "I'm really glad you asked, but..."
A key thing is to find a way to follow up when something comes your way. Whether it's something light, like the admission of a love of a certain interest or hobby or something serious - remembering who told you what and finding an appropriate way to check in is usually a good way to show you care. Be respectful of privacy. When you first hear of something, take note of how publicly it was shared, and remember the privacy "settings" for future conversation. Examples:
medical/family stuff - generally keep it private - even if it was broadcast at the big company meeting. Exception: Asking about babies and child-cuteness - pretty much every new parent wants to and expects to show off baby pictures.
deeply held beliefs - be aware of who was there when it was shared - it's probably OK to politely inquire with that group, but possibly not the general public.
Hobbies, interests - generally not a big deal to bring up in public, but be aware that some folks are super private, and if it was only ever shared with you, don't be the first to mention it.
Cultural Boundaries and Power Distance
Realize that "power distance" - the separation between people of authority and people who are subordinate can vary widely and have many implied norms that aren't obvious if you are new or foriegn to the other person's dominant culture. Western culture, espeically in the US is very low power distance. Asian cultures can be very high power distance, although global culture means that many in foreign countries will defer to Western norms here.
Or at least that's the anthropological way to say it.
What that means is that many of the attributes that you might summarize as "deferential" are more prominent and firmly grounded in some cultures than others. For a given individual, mileage varies considerably - some are happy to be rebels and join in the typical aspects of the dominant corporate culture, others will not stray from what they learned in their own cultures.
This can matter a great deal in the sense of informal sharing between team members and their manager. What one person interprets as flattering interest from a manager can confuse another person entirely.
This fits in a lot with how much question asking or joking is workable... lower power distance people/cultures will probably volunteer more information and participate in more peer-to-peer like communication with their managers than people with an expectation of a high distance/more formal communication.
Reflecting/Coaching
A really useful tool as a manager is to let a person work through the issue on their own, instead of instantly telling - that fits here, but it's usually best done privately - in a one on one. I suspect you can coach a team, but it won't come off as taking persona interest the way a 1 on 1 coaching will.
The general trick is to ask about something, listen, restate the answer in your own words, and ask a simple and very open ended question back. Generally the person can answer their own questions, but having an external ear really helps.
Probably best with work stuff, but I've used it a few times when I was in over my head in the realm of health care. Obviously if you aren't a medical doctor, you're likely, as a manager, to hit health care issues with employees that are beyond your realm of expertise. While your HR can help with the "is this reasonable?" question, the initial moment when the employee comes to your office and drops a big scary health issue on you is a great time for reflective listening. Particularly since most people involved in a serious health issue don't know the whole outcome yet, it's a great time to just help gather information and then take time to map out a plan for the person and the work they are doing later.
Talk less than you listen
Probably the hardest for me. You can tell personal stories once and a while - being the one to go first sometimes sets the tone - doing only asking and no sharing is creepy. Offering some light stories about yourself can set the tone for what's OK for your team to share.
Telling a story or two breaks the ice. Telling more stories than you listen to is the danger zone.
Addendum: Humor
An office with no humor in it is rarely anyone's idea of a good time. But just like it's important that you listen, it's important that joking be mutual. How you crack a joke is very much a matter of personal style, and an inauthentic joke simply isn't funny, in fact it's painful and awkward.
That said, here's some general joke guidelines:
You're the boss, not a standup comedian. Expressing work needs in a funny way or a quick humorous story or parable is fine. But if you find yourself going for the joke as the only form of positive feedback you get from your team - back away.
Stay away from sore spots or anything "below the belt" until you know people very well. Joking about yourself is usually safe, funny technical humor is usually safe (think of the site ThinkGeek.com), and anything you might read in Reader's Digest is probably safe. Jokes aimed at people on your team are chancy, jokes aimed at the upper management are politically riksy, jokes aimed at any protected characteristics will get you in trouble fast. The best humor is common humor that is safe for everyone to join in and laugh.
It's as important to laugh yourself when other's make a joke - it's a relationship builder. I often find that the ice is broken when someone else on my team makes a good joke and cracks me up. It shows it's OK to be a bit informal.
Some relationships never get to a joking point - joking is a form of interpersonal chemistry. There will be people on your teams that just don't share your sense of humor. Leave it be. As long as you get work done well together, accept that it might not happen.
Realize that some folks LOVE clowning around, and others hate it. The ones hating it may get quiet and withdrawn rather than say "this bugs me, I'm here to work" - so keep it in moderation and find established boundaries. For example, the end of a team meeting is fine... the middle is a big distraction unless it's breaking tension. Friday afternoons and days before holidays tend to be a lot more fun-filled than mid-day Monday.
My biggest rule of thumb is that I ask "Are we joking, or am I joking?". If my whole team is riffing on a funny idea, and I'm a part of it - great - we need those moments. But if I'm the only one making the humor, it's not the bethlakshmi show.