I am asking for your personal views of what it means. I don’t expect any general theory although feel free to contribute that as well.
What does getting to know someone mean to you?
When do you consider that you’ve succeeded in getting to know someone?
What do you do to get to know someone?
For example, for someone I kow, getting to know someone means knowing about their history, pain and relationships. It might be quite well be different for you.
In the most general of senses “getting to know someone” implies having a much better than even chance that you can predict how they will respond to a variety of situations. Trust, reliability, openness, tastes, preferences, all that sort of thing get combined and you have a good idea what makes them tick.
That can be a favorable or unfavorable impression, because “getting to know” someone else doesn’t automatically mean you will like them.
Take the people who post regularly (or maybe not so regularly) here. After a while you can imagine what and how they will say stuff once you see their name.
Can you really ever know someone? 
It is a process. Them opening up about some personal information, to me, is the first sign of getting to know them. From there it is an ongoing process. Can’t tell you how many times I thought I knew somebody and something they have done at a later date made me think… ‘hmm, guess I didn’t really know them as well as I thought.’
When I first meet people I am usually just a tad suspicious and have low expectations for them. I find it much simpler to be pleasantly surprised when I find out how wonderful they are than to be disappointed in finding out how much of a tool they are. So fair warning, when I first meet you, I’ll think you are a tool.
I like that one. You “know someone” if you have a fairly decent working model of them in your own head. If you can walk along, alone, and hold an imaginary conversation with them, and, later, it works out that, yeah, the conversation was pretty much correct.
You “know someone” when you feel safe insulting them – in a friendly way. And when, if you do, it works out right. Badinage.
I think the practice of taking the piss is fairly common ni Britain and Australia among men. Perhaps people who are/have been there can tell us about the rules of piss taking.
It’s a way of showing affection/attention in a deniable way (“just kidding”). It works to cement a relationship precisely because taking the piss at someone communicates to that person “you and I are at a stage where words like this are more likely to be fake and friendly than genuine and hostile”.
As to my question, I like the idea of a working definition of getting someone to be predicting behavior and thoughts. More specifically though, when you want to get there, what do you do or talk about?
Or when you want to get closer to someone and be more than a stranger or acquaintance, what do you talk about?
When we both lose all respect for each other.
It means I’m willing enough to set aside the time to make them more than an acquaintance. The emphasis here is on “time”, as that’s something very important to me, which I’m dedicating to them, and not something else of interest.
I don’t think it has a real end-point. It just approaches different levels of comfort and predictable behavior. Perhaps when I’m not shocked/surprised by a given response, or I can make accurate decisions on their behalf (relative to that specific person and not general actions), then I’d “know” them.
Of course, it depends what type of social circle they exist in, as well. I certainly don’t behave the same with all my friendship circles, and my coworkers would have a different perception, altogether.
Demonstrate a genuine curiosity, followed by listening and an attempt to understand them. Depending on my level of interest, it will typically involve an attempt to establish a common interest.
Also, it depends who it is. I usually don’t actively try to “get to know” people who become my friends. Those typically develop more passively. However, if it’s a romantic interest, I invest a completely different type of attention.
This is actually something that I’ve put a lot of thought into because I had sort of a shocking moment a few years ago when I realized that the way that I know a given person is apparently very different from how other people know a given person. For instance, say someone asks me to tell them about someone, even someone I am, by any reasonable standard, very close to, and I don’t even really know how to go about describing that person. My sense of who that person is is very much a concept model in my mind and I can only really tell someone about that person by sort of running simulations of that model and giving generalizations. Where it seems a lot of people prefer to describe people with characteristics, like their job, their family, their hobbies, general personality descriptors. But I just cannot provide that sort of information.
So, I would very much agree with the general idea that knowing someone means have a model in your mind of who that person is and then having a good degree of confidence and accuracy in the predictions that model produces. For my very closest friends and family, I would say I have very close to 100% accuracy, and even the situations where I’m wrong, their actual behavior in the situation still isn’t surprising. But I know I don’t know someone very well when I not only fail to expect a certain sort of response but I’m actually surprised by it and I can’t really work it in with my idea of who that person is.
As for how to get to know someone, you just need lots of good samples through interaction and conversation. There’s no specific set of questions to ask because the areas that define one person won’t describe someone else. One person may have a significant portion of who they are defined around their job where someone else just treats their job as how they earn their money and their passion is elsewhere. Asking both the same questions about their jobs will probably result in getting to know the first person better than the second. In fact, part of getting to know someone is figuring out what sorts of conversations and interactions will help you get to know that person better.
Interestingly enough, for a stranger or near stranger that I want to get to know, I find something akin to “Tell me about yourself.” to be very useful. Yeah, it will often result in some generic information about their family or job or hobbies or likes or whatever, which doesn’t really help with creating a model, but I think the more interesting aspect is what they choose to tell you about. For instance, if the first thing someone mentions is their family, that’s probably something integral to learning more about them and you’ll be more successful in understanding them by focusing on things related to family than asking about other stuff. It’s not surprising to me that people who focus on similar topics to me, even if we don’t agree on those topics specifically, are people I’m more likely to get along with and people who focus on topics I wouldn’t, even if we generally agree on them, are people I won’t really get along with so much.