It depends on the character.
But generally, it’s all about dialogue, voice and personality for me.
I start considering a character “detailed” enough once they actually start talking in my head.
And ideally, I want that for all my characters to some extent.
Long Answer
Since I have my main characters established now, most of the characters I create now are just side/supporting characters. I don’t really have a process for this–it’s either I think of a cool idea for a character (i.e. a “reformed” dark lord) that I’d want to include somewhere, or the plot demands it (I need a mentor character here, or I don’t have this type of character yet).
And then once I know their purpose, that’s when I start thinking up details, mostly their mindset and personality. This is where I struggle, since it takes me a really long time to develop characters that weren’t really there from the start. I’m better with dialogue than description, so that’s what I try to develop first. But if I think of a cool little detail, then I’ll list it down and try to show it somewhere. (I hate knowing something about a character that only I would know.)
Now, for my main/major characters? Uhh, they talk inside my head, a lot. It’s like roleplaying with myself. Sometimes my character feels lonely, and I feel lonely too. I see something they like, and they get excited in my head too. They don’t actually talk to me myself, but usually they talk with my other characters. They’ve been with me long enough for me to know how they’d talk in that situation, and naturally, lots of little details will pop up overtime. It’s both fun and annoying sometimes.
I really don’t get people who don’t bother with the little details.
They’re the most fun part of character development in my opinion, and it’s what separates them from other characters who have a similar personality type. I’m a visual person too so it’s even better if I have a clear image of them in my head, and I don’t really like adding quirks just for the sake of it.
Two of my characters’ birthdays have huge impact on their personalities actually–if I switched them up, their personalities would most likely switch too! I imagine that it’s not relevant for most characters though, but it feels really good when it becomes relevant somehow. Sometimes when I can’t decide, I’ll look up zodiac signs, birthstones, and stuff like that, but when it fits without me consciously matching them, that’s when I know that I nailed it! 
So that’s what I try to do with characters I’d like to develop, just let them talk with my other characters, or RP with other people, since for me dialogue is the best way to develop them. It forces you to think as the character, without the boringness of a character interview.
This all kinda started when I participated in one of the “Respond, Answer, Ask” threads in the NaNoWriMo forums, where sometimes we write scenes or let the characters answer the questions. That’s how I started developing my MC’s voices, which in my opinion is the most important thing after the basics.
Oh, and I almost forgot. Names! I suck at names, but I don’t really know a character until I decide on the name. I can’t start developing them without at least having a placeholder.
I’m way better when I first started writing though. I was just using my own and my friends’ names for every character without even bothering to change their personalities. Most of them were unnecessary too, just because I wanted to include them. 