I've been talking about worldbuilding, getting into the physical location and the society. Now it's time to start using this world. After all, you're not writing an encyclopedia entry. You're writing a story, so it's more about the things that happen in this world than it is about the world itself.
A lot of how your worldbuilding plays into your storytelling depends on your creative process. Sometimes, you build the world, then figure out the possible stories. Sometimes you come up with the story, then build the world where it can happen. You may come up with characters first, then figure out what kind of world they live in, and then figure out the story. You may come up with the story, think of the characters needed to tell the story, then figure out what kind of world they might live in. Or it may be a series of layers -- a bit of each, building as you simultaneously develop the world, story, and characters, with each new idea in one area sparking new ideas in other areas.
However you go about it, the world itself will show in the larger societal conflicts and in the interpersonal conflicts. You'll see that in wars and the reasons for them, in the crises that are affecting your characters (drought, natural disasters, wars, curses), the places your characters need to travel to obtain the things they need, etc. And it will show in the skills your characters have (or don't have), the resources they have, the resources they need, the way they see and interact with other people. It will show in the laws that constrain their actions and the consequences for violating those laws, as well as what the characters have to do to avoid those consequences or make others pay consequences for their actions (is there a legal system, or do you have to take justice into your own hands?). Your world will even show in what your characters eat, what they wear, where and how they live, the language they use, their superstitions and beliefs, their attitude toward authority, and how that compares and contrasts to other characters who might be from a different culture or class.
A lot of how your world is conveyed will depend on how we're seeing it. If you've ever traveled with another person and both of you had cameras, you might notice that each of you has a very different set of photos from the same locations because you notice or are interested in very different things. The perspective of the point-of-view character makes a big difference. Imagine a stranger coming into town and taking stock of his surroundings. If he's a thief, he'll notice how much wealth there is, what objects worth stealing there are, how much security there is, what the consequences might be for thievery, and what possible exit routes there might be. A poor person from a rural area might see even a relatively poor town as wealthy compared to her experience. A wealthy person from a big city may see the same town as poor, shabby, and provincial. A seamstress may notice the clothing, colors, fabrics, and workmanship, while a metalsmith wouldn't notice any of that, instead focusing on the ironwork on the buildings and the armor worn by the guards. A cook may pay attention to the cooking smells coming from houses and the variety of foods available in the market. A hungry person will mostly notice food. A weary person will home in on inns. You get the idea. What would your viewpoint character notice or care about in the parts of the world he visits? If it's not the things the reader needs to know to understand the plot, then you may need to adjust the circumstances -- change the character or find a way to create a situation that will force the character to notice the things you want to convey. I think this is one reason why thieves are such popular fantasy characters -- their work requires them to notice a lot of details, they pay attention to the wealthy as potential targets, and they move among the lower classes. That gives the writer a lot of opportunities for describing the world through the characters' eyes.
One challenge in conveying a world is that a character isn't naturally going to take note of the ordinary. If things are going on just like they always have, most people aren't going to have an interior monologue noting the ordinary details. You want to avoid the "As you know, Bob" conversation in which two characters tell each other things both of them already know. Most people don't sit around talking about the history of the place where they live or think in detail about how a device they use daily works. One good way around this is the fish-out-of-water character, a newcomer who doesn't know these things and who can ask questions -- why does everyone do that when the king passes, why does this city fear that city, how do you use magic, etc. That can either be your viewpoint character who's the newcomer and has to learn the ways of this new situation, or your viewpoint character could be the veteran who has to explain things to a newcomer. The other way to describe the ordinary is to break it. You wouldn't have a character who routinely uses a machine think in depth about how it works when it's working normally, but if it stops working, he may think about what it's supposed to do while figuring out what's wrong. If something unusual happens to break routine, then people might think about what usually happens and what's different about today. If it's a dry climate and it almost never rains, people may not think about the lack of rain, the heat, and the dust, because that's just the way it is. If it rains unexpectedly, then they can notice the difference and notice when things return to normal. Breaking the usual also adds conflict and tension, so it drives the story while describing the world rather than just being description.
Ideally, the worldbuilding should be a seamless part of your story and characters so readers just feel immersed. You want them to understand the world enough to understand the story and for it to feel like a real place. You don't want to become so enamored of your world that you stop the action to tell us all about it.
Next, I'll deal with the special case of worlds that involve magic.