In my story, one character treats another character favorably, but for no particular reason. He wants to " hang out " but has no reason to invite her, and I really am having trouble thinking of ways that she could somehow " gain his trust " without it seeming watery and cliché. Also, characters in my story are supposed to try to survive inside a closed environment ( think hunger games, snow piercer, or the maze runner ), how do I write an uprising that makes sense and doesn't get boring in two chapters?
I say explore your story's background. And your characters. Every person has a reason to why they do certain stuff, and you need to find it for your particular character. Uprising: Read news, look up political commentary, watch documenaries about countries in e.g. Africa or South America (e.g. Venezuela). Read history. There are countless ways for an uprising to start.
I'm not sure what you're asking. Are you asking how he can make her trust him, as per the thread title? Or are you asking for a scenario in which he can ask her to "hang out"? Because these are different questions really. That's impossible to say without knowing a lot more about the situation. Maybe you should think about why you think it will be boring, and then address those reasons to make sure it isn't.
It's that I noticed he trusts her and is overly nice to her above other characters for absolutely no reason whatsoever. He invites her to a high-class party, and the reason I formulated was that " He has no one else to go with " but that's still not a good reason to ask a random stranger to a party with you. The story has a dystopian theme, after a nuclear winter, humanity is forced to live underground ruled by a highly corrupt government. My main character is poor, but still loyal to the regime, and the other character is just an overly nice rich guy for some reason, even though the rich and the poor in my story usually don't mix.
So are you asking how to get her to trust him? Or why he should trust her? I would suggest you read the Wool trilogy. It has a similar plot, and details an uprising over several books, let alone a couple of chapters. It's far from boring, so I would say that an uprising over two chapters is doable in terms of it not being boring. My concern would be that it's not enough to do it justice, unless it's a very quick uprising.
Maybe he just likes her? She's pretty, she's funny, she's kind, she's smart? He feels sorry for her? He thinks she looks lonely? I mean, why does he ask her? Because he has no one else could work, unless there are other people who also have no one else? Why is he choosing her? It doesn't have to be anything earth-shattering.
The first thing I thought of is that he notices she has skills others do not have or show. In a survival situation you will gravitate toward those that have skills you find useful.
Well, from my experience, earning someone's trust is easier, and in the end more worthwhile, if it is done using simple and straightforward methods. Using convoluted processes to get in someone's good graces could rather muddle the relationship instead, and generally incites confusion and suspicion. If the main character decides to act outside his own personality trends, that would be more unsettling than if he were just to approach her casually. A straightforward person is an open person, and openness is a necessity to earn trust.
She has something that he wants. (A skill, a thing, a piece of knowledge, an organ.) She has a friend that has something that he wants. She would drive his mother crazy. She would drive his girlfriend crazy. He needs something bad to happen to someone (someone to get electrocuted to set up a lawsuit, someone to get food poisoning to ruin a caterer) and he's not going to use one of his actual friends. He needs to sacrifice someone to the Spaghetti Monster. He needs an alibi and he's confident that he can bribe her to lie.