EDIT: didn't realize I was resurrecting the thread. Sorry!
I'll give you a few examples, because they're just different instances and "usages" (as you said, not the right word!) of my Ni!
One of the most common ones is that I tell my closest friends that I can predict what they will next do, about 50% of the time. It's like a probability kind of thing. At that current moment, he or she has the highest probability to do something or the other, based on the way they are. Like there was once I went out for a movie with a bunch of friends. After the movie, we left the theatre, and my close friend disappeared suddenly. Another friend asked nobody in particular "Where's (person's name)?" And I didn't realize he was gone, but once she asked that, I knew for sure that he was inside the theatre, looking for the title of a song he heard during the show, because he recognized a song from the movie and wanted to confirm that it was that song. I asked him, he confirmed it.
Another instance in the same vein is that another close friend of mine often writes letters to me. She wrote me one recently, and without mentioning the things she was worried about at the time, I intuitively knew what she was thinking about; and I wrote back to her asking her if that was the case. She affirmed all of them to be true.
On a more regular basis, I can often predict what people will say before they even finish saying it. Not that I know exactly what they will say, but I know what idea they are trying to put across. So before they finish I know what they are trying to get at.
As a water polo goalkeeper, at the peak of my ability - there was this one instance during practice where an excellent cross was made inside to a shooter at the two meter line. (essentially, the closest you can legally shoot at in water polo) I looked at the shooter's face for a split second and I knew that I knew that I knew he was going to shoot at the top right corner, exactly at
that spot of the top right corner, and I saved that shot easily with two hands, plucking it neatly out of the sky. My teammates thought I was incredible; I walked around that day with a secret, thinking "Only Ni." That was fun.
Once my ISFJ brother bought a book called "Understanding Emotions". He was telling me that it was a great book, and that it really helped him know more about what people are feeling. Most of the book was linked to how a person's face can tell you what someone is feeling. And I told him something along the lines of "isn't that pretty easy?" (bear in mind I was very young then) He was disbelieving and tested me with a few faces. I managed to get most of them right, with a few slightly off.
On a math test when I was 11, there was a question I didn't know how to do. But something inside of me told me that I had to do this precise set of workings. And I didn't know why. But I just did it - and it came back right. Until today (granted I didn't really look at it after that exam review) I have no idea how I did it or why that answer is right.
I get what IndigoSensor said in my own studies now as well. My Chemistry lecturers and teachers tell me things and I just understand it. I drink it up naturally - from physical to organic, gas laws to organic synthesis mechanisms. The thing about epiphanies happened to me before in Literature.
When I first looked at poetry seriously, I could get stuck on not knowing exactly what the poem meant, until I read it enough times and something would click and connect:
At that moment it'd be an epiphany, like in that single momentary split-second everything flowed and connected. I knew what the poem was about. From there I could look at literary device, word choice etc and show how it helped to produce this effect in the poem. (and I feel that the ability to deconstruct, to work backwards from intuitively knowing something is the result of Ti acting after Ni has worked)
I was once really interested in this girl, but she was a complete stranger to me. I didn't even have 5 minutes of conversation with her, but she struck me as someone so incredibly amazing. But subsequently, I made a lot of guesses about her which turned out to be true - she writes poetry, her grades, her music taste, etc... And of course, now that I do know her better and I'm no longer had a crush on her, she did fit my initial observations of what I thought she was like: caring, dreamy, passionate, slightly moony, etc.
My closest friend can talk to me without talking. I wouldn't know for sure, but I think it's because I know her well, and she knows me well, and so we know what each other would most likely respond to each other. We would tell/hint each other what we meant through facial expression.
Of course... these are the success stories. There are many times I guess things about people and they're wrong. Practically thousands of times on instinct I've mentally completed someone's statements and they were wrong. That's just an example of the many times my Ni fails. But that's to be expected, I'm not someone with a predicting the future ability or mindreading.
