I will usually start with something I want for the Sim, whether it is a career I want to try out, an occult state, a new pack that I want to explore, or a tiny bit of backstory (such as "grew up rich but now trying to make it on their own").
Then it is time to get into CAS. I do tend to button-mash the randomize button in CAS just like @NRowe to get a base and then work from there. As I work, a more detailed backstory usually develops.
Some of my more recent Sims I created was a household of three roommates. I started it because I wanted to play a vampire. I was trying to go a very traditional route of what he looked like, but that was extremely uninspiring, so I ended up using one piece of clothing to create his whole personality and backstory around, and that piece of clothing happened to be a red pirate outfit from Get to Work. So everything after that fell into place pretty quickly: long black hair, long beard, pirate hat, lots of red and black clothes. Backstory-wise, I decided that he was a pirate captain from around the 1700s who got turned into a vampire by another pirate captain, and he has just been lurking around under the radar since then.
His two roommates--since the pirate captain is such an over-the-top concept, I knew I needed to make them pretty unusual as well so that they wouldn't just fade into the background. I decided that since the vampire was unemployed (so I wouldn't have to worry about him burning up in the sun), one roommate would have an active career and the other would be in a traditional career. I decided that the one with the active career would be an Actor since I haven't played one of those for a while, and in CAS he ended up with a floppy purple hat, which I turned green, and from there he ended up with longish brown hair, a little beard, and green and brown clothes that made him look like one of Robin Hood's merry men. The third roommate, to be visually distinct from the others, I decided to make a blond guy with white clothes, and that color made me decide to make him an astronaut.
Other Sims--I have a girl who is the 8th generation from her family, and she aged up to teenager just when Cottage Living came out, so she ended up with some 1920's-ish outfits to take advantage of the hat that came with that pack (I think it is the same hat that Crumplebottom wears). But she's also a mermaid, so she has a couple of tiny details that hint of that (a necklace in formal clothes, a skirt in her party outfit).
Another guy was the third generation of a different family, and I wanted to attempt the celebrity levels again, so even as a kid, I had him interested in music. As a teenager, he went for a pop-star look and personality, so I think he's one of the only male Sims I've had with dark eyeliner. He liked suits and slacks/buttoned-up shirts combos, but typically went for sparkly or unusual prints.