At my university the process is this:
Birth certificate, translated and certified by a traducteur assermenté. It cost me 50 euros for mine, plus 12 euros per copy.
A letter from your university or tutor saying that you are making adequate progress and will proceed to the next part of your course.
Next year's registration paperwork, if available.
"Quittance de loyer" or a receipt for at least the past 3 months of your rent.
A copy of your housing insurance form, has to say something about "responsibilité civil" on it.
Your passport and your visa and your 'vignette'.
A copy of your rental contract.
Bank statements for at least the past three months, or proof of your income if you have a scholarship.
A transcript.
Two copies of all of this, certifications not necessary.
This may or may not be exhaustive. It seems that this differs which each university and each préfecture.
Your first step should really to go to the international office in your university and ask them. They probably have an office constantly facilitating this. At my university, you'd get a list of the documents, and you'd make an appointment to show your documents to the university people, who would then create an appointment for you at the préfecture. (Effectively an appointment to make an appointment, bienvenue en France!).
I may have left out a few things because my visa isn't a student visa, but I know the process pretty well, and some references seem to agree.
I forgot to answer the rest of the question. Once you show these documents to your university, they will create an appointment for you at the sous-préfecture (or an antenna office thereof). You will then show up, hand over everything (with two copies of every document and all of your originals as well) and hopefully get your first carte de sejour (a visa and a vignette in one). They will also ask you to bring an interpreter if you don't speak French very well. Go early, because they threaten to cancel all appointments for which you are > 5 minutes late.