The T/F conundrum is that Ts (regardless of E/I range) seem to work off frustration by verbalizing it, or at the very least, by physical-izing it: snapping at people, slamming doors, stomping around, being generally irritated. Ts are more likely to let that expression be the end of it, though; nobody can hold a grudge like an F. (Ts, in general, don't see the emotional as worth the effort of sustaining for a long time, which is why Ts tend to have short, fast tempers while Fs do the slow burn.) The problem with T-expression is that the F is likely to flinch, and the more sensitive (or insecure, or just not-at-ease right then) F is going to feel like s/he is being hit with a ton of angry bricks every time the T opens hir mouth. The F remembers/stores the high/negative emotion, and feels like the T just walked in and dropped a whole case of ANGRY on the F's head and walked out again, feeling much better now, while the F is crumpled up in a ball feeling like crap.

The only way to deal with it as a T, it seems, is to at least thank the F for listening and/or allowing the dumpage. Nothing motivates an F better than "this really matters to me (that you do this)".

To motivate an NT, you only need to say, "well, I'd ask you, but you probably couldn't do/handle/manage it. Too big of a challenge (or: above your grade)" -- and you'll see the NT (especially ENTJs, who fall for this trick EVERY SINGLE TIME) go ballistic to prove themselves as capable. NTs have a big thing about competency, though ENTJs and INTJs are the worst of the lot for that. NFs just want to connect, so if you tell them, "you can't do this," they take it personally and agree with you, and slink off to a corner to lick their wounds (or, alternately, to sulk, ehehe) about the fact that you spoke so harshly as a sign that you don't like them. The NT could care less whether or not you like them, so long as you respect them (and think them competent).

I once had a boss ask me why it was that CP could motivate his disparate team so effectively -- boss being, I suspected, a strong ESTP. I ended up doing a crash course in MBTI as a general management rule-of-thumb, because CP-the-INFJ could peg each employee instinctively -- being a people person -- as to what would motivate them. For someone less emotion-oriented, the MBTI is a useful tool to compensate for what is not the natural inclination. (I say this as someone who will sometimes lean hard on basic MBTI knowledge to compensate when I'm new to a work environment, because I am not a natural connect-to-people person.)

My reaction to "someone who puts people/feelings first" is that I think I put people first but not feelings first.

Err, my bad -- from an F's point of view, they're the same thing, basically. "Other people" = "feelings about/between people" = "making decisions based on emotions (for/about/due to other people)". A T is not a heartless machine, and certainly is going to think about other people (especially NTs, who are going to be juggling the iNtuitive need to take in information, and what are people if not a great source of information?) -- but the ultimate decision process is not based on how other people feel, so much a more head-ruled, logical, objective-attempt at understanding, though how people may fit into the decision certainly comes into it -- but a strong T isn't going to decide based solely on feelings, just as a strong F would feel very uncomfortable with a logical/objective decision that didn't take into account how s/he and other people will feel as a result.

A T can be incredibly generous, for instance, and the F will feel all warm and fuzzy. If the T is less socially-adaptive (like INTJs and INTPs can be, sometimes), the T might forget the F-ness present and say, "well, actually, it's just that it's on my way, and by doing this, then I know you'll be willing to do that in return, and besides, I also get this out of it," and is all pleased for finding both objective (benefit) and subjective (happy friend) out of an essentially logical idea.... and the ENFP in the passenger's seat feels utterly, completely used -- because they hadn't even thought of "what I get out of this" and were just enjoying friends doing stuff for friends. (Actually, this will crush an ESFJ even harder, because they didn't even see the possibility of the benefits, or even, sometimes, the pattern of the NT's thought processes.)

Uhm, I guess I'm giving the impression it's really easy for an NT to crush an F. I'd say something to alleviate this impression, except... it's pretty much true. NTs do have a knack for accidentally stomping on Fs -- but then most Fs I've known have instinctive sense for how to damage an NT in return. Heh. Goes around, comes around, eh.

Mostly what I do is think about how it's connected to other stuff.

That there is the ultimate clue that you're an N -- the stronger the N, the more likely you are to see everything as connections and possibilities.

(As opposed to the S, for whom facts are facts and possibilities/potentials aren't a focus... meanwhile the N is going, "but if you add this fact to that fact and see how this parallels that, add this other fact and OMFG we could end up with GODZILLA!" and the S just stares blankly. Not that I've ever had that experience, myself. Righto.)