In addition to the excellent advice in multiple other answers (which are worth reading, but which I won't try to repeat), I'd like to throw some additional perspective in your direction, which might also answer some more of the questions you asked.
Scope your problem.
I don't know the first place to start with who to ask or even the right questions to ask.
The right questions to ask are the ones that will provide you with the answers that you need to get your job done.
However, it sounds like you only have a very loose idea of what this job is. "Document." Okay. But what are the requirements? What deadlines must be met? What level of "documentation" is sufficient, so that you can determine when something is sufficiently documented, so that this task can be declared done? *
Never significantly start your efforts a major project, especially one that people will be expecting to have significant benefits from, and especially one that will have some notable costs (like interrupting other staff members), until you have some of the basic boundaries determined. Sometimes ill-defined projects don't have clear boundaries, but even in those cases, a guideline like "Make Tom happy" will at least give you a place to start (even if it is a very vague place, such as simply knowing that Tom will be the person to ask).
This is a great case of being given a task where you don't have enough information, and it isn't going to look bad on you because there was no way for you to have this information (because, until recently, you weren't a part of the company). Your ignorance will not look like incompetence. On the contrary, by demonstrating your astute awareness that you don't have enough information, you are actually showing competence. And hopefully your questions will give you answers so that you can identify some specific needs that you can then start to figure out.
- Note: documentation tasks of changing systems might never be done. Still, you can potentially complete a specific task, such as completing an entire pass and knowing how long the documentation is predicted to remain relevant before another major company-wide pass is likely to be needed to completely overhaul the results of the current documentation work.
Note 2: While some other answers point out that this can be a great task that caring management can assign a new person, this easily could be a case of a decision maker deciding, "I don't know what to have this new person do, so let's just assign them the documentation project, because that's unlikely to irritate customers or cause any other problems. In either scenario, this is a task that will produce some results that a competent manager may review closely. Also, your questions may result in some people needing to be accountable, so that could cause some friction which may be of some interest to management. Do expect a very realistic possibility that you may be significantly judged on this project.
If you shine, this project could turn out to be a great opportunity to look invaluable (in the positive sense of the word). Put forth some good effort.
Again, if you haven't yet, I do recommend reading other answers because this question has led to some excellent responses by other people too.