It takes the situation/information presented by Ne and judges how it's important to me, and if it is important to me at all. Then I discard what 'feels' unimportant, or put it in the 'maybe later' pile.
I've only now started to implement Te to sort out which pieces of info I will be executing what with, and using Fi to determine if the ideal that it holds is doable in reality using Te and if the standard that Te is working at is good enough for my Fi (and whether or not there's any way of raising that standard without it costing me an arm and a leg). I usually use my INTJ to verify this process though as it a) drains the life out of me, b) is new to me and therefore subject to mistakes, moreso than my process with people and c) his Te tends to be able to take more shit onboard than mine, which in turn teaches mine how to deal with shit.
With people, I take the information that Ne gathers while getting to know them, and later on Fi processes that information. I reserve judgement at that point as I want to see the complete picture first. I put together their personality in a 'logical' way. If they do that, and say that, combined with what I know from their past and the bodylanguage they were vibing, not to mention the situation they're currently in (stress at work, at home, problem with friends that are present, whatever it is), then it logically follows they value this, believe in that, see the world in that way and therefore will respond [insert reaction] in the event of [insert situation]. If I'm lacking info, I store the puzzle away along with judgement, and send out Ne to retrieve the rest of the info. Once the picture (and this picture can be the picture of just the part of them that I interact with regularly, though I try to get the whole overview of their personality if possible) is close to fully complete, I decide what I like, what I don't, what my relationship with them will be like, and how I will meander around their quirks and how they're likely to respond to mine. If, along the process, I already discover a part that is likely to be incompatible with me, I'll intensify the research on that, to make sure I didn't miss anything and resolve the issue, before I decide to stop progressing the relationship beyond what we are at that point (acquaintances, casual friends, mere strangers, even closer friends can get bounced a step back at that point).
If at any time, I'm unable to gain access to the person in order to get more information via Ne, I'll use Ne to dance over the gaps and give a number of options which could fill the gap, and Si giving me a record of the previous behavior patterns in others who are alike this person as well as the person themselves, so Fi can determine which piece of info is more likely to fit. If this is done a lot however, you get crude estimates, instead of actual personality maps, which is what my goals is, so I do not like doing that. I will however, if I'm forced to make a decision before I'm done, and I'll feel annoyed and irritated at it, knowing that my work isn't as thorough and complete and that my conclusion is likely to be somewhat flawed.