I try not to think of it as "world-building" so much as "discovery." When I start working on a story, I normally have some basic ideas I want to touch on. (ex. "story about one man's struggle against the shadowy guild that raised him along with his transformation and growth." or "I like a lot of supernatural fiction. Vampires and werewolves are cool after all. If I could make my own rules about the supernatural, what would they be?")
Then I hit the ground running. In the case of example A with one man's battle, I just start telling his story. I have a few vague people and places in mind. I give each a name as it comes up and then keep working out. As the protagonist travels and gets involved in bigger things, he sees more of the world, so I have to start developing the next town, the neighboring kingdom, the next continent. If I decide the character is going to gain direction from a religious source, I need to know what the main religion for that area is, then keep that in mind for each area he encounters. Major religions are rarely world-wide. Make sure you find things that either separate one region from the next (one culture is based in the standard medieval fantasy variety and the other is a blend of Japanese and Egyptian) or find reasons why two regions are not so different ("Those bastards across the river? Was part of Ghalor until some baron or other got uppity 40 years ago and started this damn war. They live like they're still Ghalorans, but I'll be damned if I shake hands with anyone what don't bow to Queen Loryia.")
If a random idea comes to me, I always make sure to try it out and see if I can make it fit with the world as I discover it. If not, take it back out.
Above all else, feel free to dream the world you see. Uncover it through imagination so you can see through the fog of reality to find each piece of this place. Your world. And like dreams, never forget the two most important things: anything you want to find there can be found if you look hard enough, and it's always under your control.