The first thing I would do is become a member of
ASLOCA which is an association for tenants. A donation is required, and there is a small charge per consultation. Make an appointment, bring your contract etc and they will assist where they can.
They are
very helpful, and will give you clear advice (including form letters) on what to do, especially if your regie or landlord starts misbehaving.
For notice, you usually have to give notice in writing being specific with your date/month of departure at least 5 days before the end of the current month. I strongly advise you to go to the post office and send the letter
recommandé, and then also send it to the regie by fax or by email.
Once you have moved all your stuff out, you will have to give the apartment a thorough clean and put right any damage (no matter how minor). There will be an inspection (you can ask a representative from ASLOCA to be present, also strongly recommended) and the regie will try extremely hard to dock as much as possible from your security deposit.
In my opinion the system is designed to be intimidating and always remember that the regie is not usually your friend. Work with ASLOCA, don't let yourself be bullied, make sure that you've done a little work in advance of the inspection, and things should go smoothly.
Good luck!