The essence of narrative debate is controlling the explanation for why things happen. In each topic, you develop a narrative that extends beyond just what the topic is about, but focusing on core ideas that present a worldview you can use in-round. You've got two goals: first, to present a consistent advocacy that's logical and sound, and second, to make sure your advocacy has the best explanation for everything in the round. This is partially adapted from a lecture given by Devesh Kodnani, and additional elaboration can be found here in a video from Beyond Resolved.
You can make different arguments in a round, but they should all be coming from the same place and should not contradict each other. This isn't just explicit contradictions, but about your worldview - if in one speech you argue that the US should reduce its military capacity and in another speech argue the US needs to take more aggressive action. Most importantly, your arguments should be coming from the same place - they should fit within the general theme of your argument, and should all lead back to your side of the resolution. Every second you spend on arguments that are unrelated to your narrative is a second that's distracting the judge from the message that wins you the round.
Use your worldview to cast doubt on the causes of the arguments they talk about in their case, as well as the solvency they claim their side provides. This goes beyond cross-applying your arguments - you must do the work for the judge as to why your side is a better explanation. If the judge sees the best explanations in the round coming from your side, they'll very likely vote you up, especially in close rounds. If voting for your account of the arguments in the round can sufficiently address both the problems you and your opponents identify, it's likely they'll vote you up.
However, it's not just enough to address the problems. You need to explain why the narrative you have gives a better explanation of the causes of the events your opponents describe. This is where having a narrative is crucial - you need to explain not just why your argument has the potential to explain your opponent's issues, but why it's the better explanation. This requires logical warranting of your claims and often comparative weighing of your links against your opponent's.
Without explanation of the round's issues, the judge finds it much harder to vote for you. Affirming may prevent, say, China from expanding and attacking other Southeast Asian nations, but that vote leaves unresolved other issues in the East China Sea. Connecting your arguments to both the cause and effect of those issues allows the judge to select the side that has a clear worldview - why these problems arise, and what's best done about them. Your job with the narrative is to make sure the judge gets that from you.
Why is the judge voting for you?
At the end of your final focus, the judge should be able to easily sum up the reason to vote for you in a sentence or two. To make this crystal-clear for them, I recommend starting every voting issue out with a short summary of the argument. This clarifies your advocacy, and should be in your own words with clear warranting, without relying on cards or a tenuous link chain. (You'll notice this should shift your choice of contentions and turns towards clearer, more explainable arguments - this is a good thing. Really squirrelly arguments are not very convincing, and are hard for a judge to intuitively grasp.) The ideal summary and final focus should mirror each other in their discussion of the main voting issues of the round. Most judges don't vote on blips, so make sure every argument you go for is clear, warranted in every speech, and fits into an overall narrative for why the judge should vote for you.
Questions to ask yourself
"Does the judge know exactly why they're voting for me?" The judge needs to be absolutely clear on this throughout the round. To help, use ballot-directive language in your later speeches, especially when extending offensive arguments (e.g. instead of saying "extend our first contention," say "vote on our first contention").
"Am I making important arguments?" Not every argument is worth making, and not every argument you make is worth going for. This especially applies to blippy turns that teams read in the hopes that the opponent drops them. Unless they're significant enough to be weighed against your opponent's arguments, why are you making them in the first place? Arguments you go for must be important enough to be worth your time. Otherwise, not only do you waste time, but you distract the judge from the arguments that are really important.
"Is the debate happening on my arguments?" By effectively making your arguments around your narrative in every speech, you signal to the judge that your arguments are the important ones, and ensure that the deciding factor in the round is who wins the arguments you make. When the arguments that matter are yours, not only is it more likely you have the main offense in the round, but your speeches are all tied together with a clear story for why the judge votes for you.