Apologies to all for the length. I rely very heavily on my Ne personally and professionally with significant success, and I'm fairly confident I'm not an ENFP for reasons I elaborate later, so I hope this is of some value to the INFP crowd.
@FreeBeer, what you said resonated strongly with me; do you find you can overdo Ne?
While I can do all of those things, I end up spinning faster and faster, getting less and less really done, and reaching a point where I reach a state approaching panic (or even worse, dissociation) due to the amount of input that isn't evaluated fast enough by Fi. So while my Ne works very well, thank you, I need to regulate my use of it carefully, whereas I can use Fi endlessly. "Fi binges" recharge me, whereas Ne burns me out, but that's also external interaction in general for me. If I evaluate Ne input using Te more heavily, it just makes the wheels spin out of control even faster (and my judgement goes to hell). Sometimes it's useful in small bursts, but on the whole, it wreaks me.
As for developing Ne, do we mean having it be more sensitive to input, having it be more accurate, or relying on it more of the time? For me: Sensitivity is a matter of quieting down other ways I process input and putting a little trust in Ne so it opens up past whatever resistance is in place. Accuracy is a matter of patiently watching things unfold, becoming mindful of my biases (including confirmation bias), then deepening my understanding to fully accept what I observe has happened. Reliance can be easy to acquire too quickly. If that happens, I lower my trust in my intuition and strengthen the mental tools that improve intuition before diving back in, lest I be an example of the Dunning–Kruger effect.
IMO, effective intuition comes from a well trained unconscious mind. A lot depends on having acquired, stored, and using a lot of knowledge, beliefs, and experiences in a highly connected, relational way. I find absolute truth abhorrent, but it might work for others. Keep in mind that until an individual's definite understanding gets close to the readily available expert human understanding in an area, intuition often isn't immediately useful. Even google often outperforms it. However, this is an ideal training ground if one takes the time to exercise that intuition before seeking expert answers.
You'll know you're getting somewhere when your intuition leads you to deeper questions, whose answers get you closer to a solution. That is, intuition isn't just about seeing answers/outcomes, it's very important in offering questions/perspectives. You'll start making little jumps that others didn't anticipate. With skill, this becomes more of a cascade that rapidly diverges from any initial course, and you'll need to ensure other functions are well trained to keep you in a useful pursuit.
I believe I solve rational problems something like this: I pour observations and statements being made in, wait for feelings to fire, dig around in there until I tease out what feels wrong, listen to intuition of which way to go from there, and when I find a solution that feels plausible, I finally have to dig out my thinking skills and "do the math." (It's generally hard to communicate to another until this is done, alas.) Finally, act or communicate results. Rinse, repeat.
For non-rational problems: Same but minimize the thinking part, so it's a simpler loop. If there's significant perceived danger in that, I tend to do more thinking. Lately it seems that thinking can be quite reductionist and tends to worsen my decisions by narrowing my field of view. Sometimes it does help me spot incompatibilities in my beliefs, which is important to me, though it's of little use in resolving them.
Where this all breaks down horribly: When it's entirely clear exactly what is needed from me, and this actually reflects reality, or when there is significant denial of the reality I see without refuting it effectively. Or when the future doesn't matter much to others. My productivity plummets, nothing I do is motivating, and I spend even more time coping with that stress than trying to force myself to do the work that I can't use my normal tools to navigate. It doesn't even matter to me in these situations if the work is good. It feels utterly pointless and I can't feel good about it.