If I understand correctly, your mission is this: you want to play a tabletop RPG, you want to do that with your sister as one of the participants, she'll be the only player, and she wants to play as a character like Raven from Teen Titans. (Awesome!)
For a basic introduction to roleplaying, you ought to read through this: What is role-playing, and where do I start?. This teaches you some more you might want to learn about how roleplaying games function. Having seen a bit of how people do it in one game is going to be helpful for you.
Choosing a game system
Beyond that one of the things you're going to want to consider is the choice of roleplaying game system. This is an awfully broad market, with thousands of games available, and choice of system can be really helpful. Think of it being like the board game market: there's stuff like Chess, Go, Monopoly, Risk, and thousands of others, and all of them offer radically different gameplay. Even ones that look kind of similar (chess vs. checkers) can wind up playing out extremely differently.
Most people skip the question of system though and jump straight to D&D, because it's what a lot of people are already familiar with, and people consider it to be potentially suitable for absolutely anything, or at least, with the proper adjustments. It's not really though, and that's a bit like picking Monopoly when you really want to play Risk, under the assumption that if you just change it enough it'll be enough like Risk anyway. (You might as well just play Risk.)
D&D's pretty good at fantasy adventure games about heroes killing tons of monsters and taking loot. It won't do superhero games all that well. It takes an awful lot of effort and knowhow to get it doing anything else, but for other things you'd like to do there's probably a game system that already does that thing. Most of them nowadays don't involve considerable time and effort to learn; D&D with its three books and many supplements takes an extreme amount of time and energy to learn compared to most of its current competitors.
In your case, there's several popular superhero games available. Some like Mutants and Masterminds are just based off D&D (as many games were from the 90's). There's one that's perfect for what you're doing though.
Masks: the game for your mission.
In your case, I would suggest going with Masks: not only it is a superb RPG based on an extremely popular system (Apocalypse World, which produced the Powered by the Apocalypse system), it's already set up for basically playing out Teen Titans and even Raven herself. You can get it from Drive Thru RPG as a PDF; currently it costs $13.99.
(I'll warn however, not knowing your age, that Apocalypse World itself isn't a game for kids, since it deals with a lot of fairly mature stuff. Masks is fine though and doesn't deal with the same topics, genuinely being shaped for teen superhero stories and being age-appropriate for them.)
Masks has a few types of characters available, which we call Playbooks. The playbooks are available for free from the manufacturer (PDF link). Several of them should be reminiscent of a few Teen Titans characters and that's not a coincidence: the first playbook is The Beacon, who's very much like Robin (plus some other heroes); The Outsider (PDF pages 15 & 1 6) is like Starfire.
There's a playbook that's basically made for Raven: The Doomed, on PDF page 7 & 8. (The Nova, pages 13 & 14, could also apply.) The Doomed helps play out Raven's character arc, her struggle with her own origins and nature, her exploration of her value to others, her emotional issues connected to what she feels is her inevitable fate. Check the Doom and Doomsigns mechanics on the playbook's second page (PDF page 8) and look carefully: a character modelled by The Doomed is eventually going to tick off that sixth doomsign, "Your doom arrives; confront it and perish." As in the original Teen Titans series, this may be more of a metaphorical perishing than literal — or both at once. You and your sister will figure it out as you play.
Part of why I'd also recommend Masks, beyond pretty much being designed for the story you want to explore, is that it's going to help you learn how to GM. In fact it's going to show you pretty explicitly. The Masks rules for GMing the game give you soft & hard moves, and tell you when and how to use them. These soft & hard moves represent nearly everything you'll be doing throughout the gameplay as a GM, such that the game is basically recommending you options as they come up.
That system's also going to help you and your sister explore the story together, as it will give your character considerable room to guide the story in directions she wants it to go. That's a good thing: not knowing which direction players want the story to go in, and trying to guess and adapt for them, is a common issue GMs run into, and this game does a good job of providing a solution to that. (There are other games that also do this very well.)
Masks is going to play out extremely differently to D&D, and has a different ruleset. Principles you've picked up from D&D may not, and often won't, apply. It's a different game to be taken on its own terms. You may or may not play an NPC; you don't actually need to do so at all. If you do so, you'll be portraying other characters through your GM moves rather than through a playbook & player character.
Learning the ropes can be tricky.
Basically the process for all of us is sorta like this: go into our games so nervous we might even be sweating or shaky, hope we do well, play out the game with our players, notice all the places we totally rubbished up or forgot things or made mistakes... and it usually results in the players (or in your case, player) having lots of fun anyway. They weren't noticing all the mistakes you noticed in yourself, and were just enjoying portraying a character.
If your players enjoyed themselves, you've succeeded as a GM. Good job. Take the mistakes you noticed and use them to learn and improve, but don't get hung up on them. They happen, and you're doing something new. You'll keep noticing stuff you didn't do as well as you could because we're always improving as players or as GMs.
If you have other questions you can ask us, discuss stuff on any number of forums including the official Powered by the Apocalypse forums, and you may hop into our site chat to talk with people with experience in various games, including PbtA and Masks.
Finding other players
The Apocalypse World engine & games like Masks are fairly popular, so you can actually reach out and have a decent chance of finding other people to play with including your sister. (As mentioned though, Apocalypse World itself deals with mature topics, so you may not want to play the base game depending on your age.) On this site we have a finding other players tag you can browse through, to which these questions will be of particular relevance:
If you do want to stick with just playing between yourself and your sister, that's also fine. One-on-one/twosie games can be pretty great.
Best of luck & have fun.
