Advising a high school research project I have been contacted out of the blue by a seemingly highly motivated high school student who has requested the opportunity to do a research project under my supervision (in the field of stellar astrophysics). I am not opposed to supervising such a young student, but I fear that they will lack all of the prerequisites to even get started on any kind of project. 

How should I approach this?
I supervise high school research students every summer. It is very rewarding. But, it is a lot of work, so keep that in mind when deciding whether this is something you are interested in.

Besides for the obvious issues (lacking background knowledge, field-specific skills, and other preparation), I find that high school students tend to need more emotional support from me than other students I work with, so that is something to consider as well.

I interview the students and ask them questions to assess their personalities. I look for the following qualities specifically in would-be high school researchers:


Good attitude. Younger students can be a little bit immature, and this often manifests as a bad attitude. Working with a high school student who does not have a good attitude, does not take criticism well, and is just generally unpleasant to deal with, is just not worth it.
Willingness to fail. The high school students who do research are used to being very successful at everything they do. Sometimes, research can be paralyzing to them because they aren't going to be successful at it immediately (or even after lots of work).
Works hard. (Obvious prerequisite. Without hard work, they will not be successful and working with them will be a waste of my time.) 


The high school students I supervise come to me through a K-12 outreach program run by my university. (When I am contacted by a student "out of the blue", I tell them to apply to that program.) As part of that, they commit to five weeks of full-time research in my lab in the summer. After this, some continue to work with me after school during the academic year. I would not agree to work with a high school student who wasn't prepared to make a specific commitment and identify in advance exactly when and for how long (at a minimum) they'll work on the project, because of the high probability that it would end up being a waste of my time.

Designing projects for high school students is actually similar to designing projects for undergrads, because the very strong high school students have a level of preparation that is similar to a typical undergrad sophomore or junior. The basic characteristics of such a project are:


It should be appealing to the student. (I want to encourage them to get into science, not scare them off by giving them a niche project with very little general appeal.)
It should be something that I am 100% confident I could do myself, if I had to. I should be able to plan out (roughly) in advance what they will do each week that they are with me, and even prepare general instructions for every week in advance (so that they are never waiting uselessly for me to tell them what to do next).
They should be able to start doing some useful work after only a few weeks of topic-specific preparation. I give them very focused homework - lecture videos to watch, things to read and answer questions about, tutorials to go through - and expect them to do that mostly independently before they start.
It should be a project where they will be able to make some progress after about five weeks of work. 
The project should have potential to turn into something bigger, in case the student turns out to be amazing!


I also have a bunch of material about doing research in my field, and about expectations I have of students I supervise. I've prepared these for my undergrad students, so I already have them on hand for the high school students. It is very helpful for them to have these as reference.

P.S. I have co-authored two papers with my high school students. Don't underestimate them :)