This is a hard one to describe, and I feel like it varies between projects and characters for me. Often times if I'm trying to think up a character I have some pre-existing features or elements I'm interested in (anything from prosthetic limbs to freckles), and there's some remixing that goes on. I may browse through photos of models or otherwise to help me complete the idea of the character.
Pinterest can be really useful for figuring out theme/aesthetic/fashion. I mostly go there for clothing ideas.
I don't really worry about them being distinct or interesting, I just focus on the visuals and characterization making sense together and in the story.
I feel like this just comes naturally usually? You put bits and pieces of a person together in both the physical and mental sense, and more and more you find it all coming together. Sometimes it doesn't turn out the way you first expected, though.. In terms of my characters, for HH there are three leads. Asoro, a fallen angel, who is very sweet and kind, is drawn with a round face and round eyes, his coloring is very earthy, with wings modeled after sparrow, rather than the traditional angel look. The other two characters, who are hell hounds, or more physically imposing, both with dark hair, and very simple clothing with minimal color usually. The hounds generally wear shades of grey plus blue jeans, and the angel wears off white with a touch of gold, and I'm slowly introducing more color into everyone's wardrobe as the characters get closer (there's also increasingly lovely flowers left on the kitchen table in the vase, which was originally empty, but no one has picked up on that ;D)
Admittedly designing an angel that looked angel-y but was also going to not loot weird in an Earthly setting was difficult. But the results are what they are at this point. I didn't really take him being a principality into consideration enough when designing things, which works fine for the majority of the story, but would have been a nice touch for a flash back/exposition-y bit.
I'm sorry this feels very rambly. It's hard to write it in a way that's useful advice for others. 