How to write about an area I'm going to study in undergrad research? I'm a undergraduate student in mathematics and I'm applying for a scientific-initiation (or maybe undergraduate-research) scholarship in which I'll study a certain topic in mathematics (so I'll not really do any research, despite the name of the program). 

To enroll in the program, I have to submit an eight-page project describing what I'm going to do, with a schedule for the duration of the program, methodologies, and references. Formally, the project text must contain a summary, introduction, objectives, methods (or methodology), a schedule of activities, and references.

For the methodology/methods, I'll just say what I'll do: read the theory in the main reference text, maybe rephrase some definitions or results and make some additional remarks, do the exercises, maybe construct some new examples/counterexamples. I think it's a bit too direct but I'm not very concerned with this part. The same applies to the references.

My problem is: I don't have any knowledge of the subject (beyond the very basic) I'm going to study (and don't have time to further study it until the deliver of this document), so I don't know what to say in most of this document sections. I'll just pick a book on the subject and study it. In the summary, I quite already said that, and I don't really know what to write in the introduction and objectives.

I'm a bit concerned of talking about this to my advisor, because we already talked and it seemed clear that I should write the document all by myself. Maybe it's just me not being able to write down some very simple things of what I'm going to do.
In most of these situations, a large part of the "exercise" is for you to grapple with the writing of that document yourself, thinking about the various aspects.

It is to be expected, or even hoped, that you feel you are unable to do this, due to lack of information, and lack of experience.

Then, talk to your advisor for hints and advice, and show them what you have written, _in_your_own_voice_... as the starting point for further progress.

That is, there should be several/many iteration cycles in creating the document, and, yes, you certainly do need your advisor's help... but in refining and redirecting your own thoughts and preferences.

Good that you recognize that you don't really know what to do, having had no experience at this, but a large part of the experience is to try to do a thing you've not done before... and partly fail, get help, fail less, get more help, fail less, rinse-lather-repeat. :)