I'd suggest from a technical standpoint of reading up on shortest path algorithms and the like. Depending on the structure of the problem and the tools at hand you can make solving this kind of problem harder or easier. Once you've decided on the basics, such as
- Is the destination known? Many people climb mountains, solving the problem of getting to the top is a matter of smaller survival and directional problems. Same thing could apply to mazes.
- Is the style of maze something that the character could innately grok? You could have all sorts of cultural "explanations" for why something is the right choice.
- Is there a map? This is the easiest way to handle it. You can use a map like a time bomb plot piece. Where finding pieces or deciphering the map as you go creates a time lock that keeps your story on track.
- If it's merely a geographic problem, then keeping track of your location with landmarks that you can see (the sky, a mountain in the distance, where the sun rises each day) might confirm a person is heading in the right direction
- Level of technology. You could send bots to "crawl" a maze if you're in a sufficiently advanced civilization. You could go up in a hot air balloon if it's an exposed labyrinth and create a map. Or, if it's a period peace that doesn't have this sort of capability, then you need something else.
All of these are technical and solvable problems:
To do this successfully in a story, you'll need to ultimately have some sort of conflict. If solving a maze is trivial, then it's not a conflict. I'd worry far less about the technical details of how does one solve a maze and focus more on how the maze interacts were her emotional state and what it tells us about her character.
- Establish a goal for getting through the maze
- Ensure there's a conflict. This will either be internal, external-antagonistic, or Woman Vs Nature (She vs Maze)
- Give her a character arc and allow the conflict to change her as she moves through the maze
Any technical details you choose to use to solve the problem should serve those three points so that you have a story and not a how to solve a maze guide.
This question was super broad and could be boiled down to how do I plot a book. Because ultimately every plot is a character moving through a maze of some sort. Here are three examples of different ways to solve a maze and conflicts that could drive the story. This is what I mean about the other elements being more important:
A person is locked into a maze, the environmental hazards of not having food and water sources creates a time lock. Their method for solving it could be entirely logical, but the conflict is whether their ability is enough to solve the maze in time. The tension of someone who knows all of the rules, but who may not have all the supplies drives the story forward.
A person needs to get through a maze to get to a McGuffin. They have a super power that allows them to see the lives of people who constructed objects that existed in the past. The conflict is that they have to relive pieces of the lives that lead to the maze being built to get through it and learn the way out. the McGuffin becomes less important than the personal story of how and why the maze was created and the conflict of the past which is now echoed in the present through self reflection.
A person has no idea how to solve a maze and is chased into it by an antagonist. This thriller features the protagonist simply trying to get through it to survive and the plot conveniently uses the maze to block or allow the person to escape by the use of their raw wits. Occasionally they lose at some small task and pay a price, but the maze escalates the problem as the story goes on. The climax is where the person finally "finds a way out", but must overcome the antagonist with all of the things they've learned since they entered the maze. Queue comedy or tragedy based on the success of this move. In this story, the person doesn't need to understand mazes.
The technical knowledge of how to solve a maze is only as important as that is to creating a character or situation that is worth spending one's time following. You can have as much or as little knowledge of mazes as you want and still write a compelling story involving one.