What are the best questions to ask when you really want to get to know someone?

The ones to which you are actually interested in hearing the answer. It depends how much you know to start off with. If you have just been introduced to a total stranger, sometimes it is useful to ask about something which you have some familiarity with, so you can have a conversation. Given that it can produce awkwardness if you start with politics, religion or sex, best to keep the subject neutral; a hobby or pastime, food, the weather, media gossip are safe and relatively anodyne. If you want to grab their attention, ask about something a bit more risky, or be unusually direct. Don't ask what someone does for a living unless you actually want to know. Even then, be aware that much of the time people ask this question but actually mean 'how much do you earn?' This is so they can contextualise you in relation to themselves and find an easy pigeonhole to place you in so a power dynamic can be established. If you have travelled a bit, you might ask "Have you been to Europe?' or 'Have you visited the Grand Canyon?'. If you look at a person carefully you might see some cues which might help. Learn to be observant. People often like talking about their pets. If someone has dog hair on the slacks, you might ask if they have a dog (you have guessed the answer, so you have a conversational gambit). Best advice; use your eyes and ears, and look for a cue to an entry point, then take a punt.

I would really like to know more about you. Would you be willing to help me do that?

What motivates you?

The question answers itself. Ask: "What are the best questions to ask when you really want to get to know someone?"

I’m guessing that ‘learning more about someone’ is being done for a purpose because if you are investing the time into querying someone it is usually being done for a reason. Maybe the reason is romantic or thinking about starting a friendship or sucking up to the boss or casual conversation. The best questions to ask depend on what your purpose is. If you’re sucking up to the boss you are going to want to ask questions like “Isn’t it true that your prowess, in such and such, is magnificent?” Casual conversation would be "So, tell me about yourself" If you’re looking at a possible romantic partner or a potential friend then the questions seem like they should be more specific: What are your beliefs about honesty? What is your political stance? Are you religious? What do you like to do for fun? Do you want go with me to do such and such? Questions, in this circumstance, should cover the areas that are important to you. I’m thinking that you get to know someone by filtering questions manufactured by your own perspective about things that are important to you. Basically, I’m guessing, your question depends on the type of things you would like to know about the person.

Those which will allow you to determine if the two of you have anything in common! Also questions that will allow you to find out who the person you have met truly is and what is fundamentally important to them.

Truly listening and being present is the best way to learn about someone.

A simple "Tell me about yourself" is a good way to get the conversation started if you know that the individual wants to talk. From there, you ask more questions based off the answers given.

If you had the choice to be invisible or have the ability to fly, which one would you choose and why? The insight this provides to a personality is generating far more than one bargains for.  For instance, you may get a reaction similar to, "I'd be invisible so I can hear what people say about me when I'm not there." That tells you they are very self-conscious and concerned with what others think of them. On the other side, you may hear, "I want to be able to fly so I can go to the beach whenever I want," you find out their travel desires and that they are more than likely someone who is a free spirit. Lots of possibilities here.  The best part is that the "why" opens up a whole line of questioning to figure out more about how someone thinks.