It's all explained in plain English. The only thing it doesn't say (and I wished it did!) is how many hours per week you are studying and how many weeks in total the course takes.
First, you must pay 770 € to pre-register. That will get you your registration certificate document which you bring to the French embassy/consulate.
Once approved, you'll get a long stay visa (the site doesn't mention how long though, I'm guessing 6 months or 12 months. The course I imagine goes for at least 6 months)
Then you show the AF your passport (with visa stamp in it) and other documents, pay the balance of your school fees and away you go!
If you are at mid A2 level when you get there, you take the French Language and Culture Programme which takes 597 hours to complete and costs 3,582 € (woah!). It should take you up to C1 level (which sounds rather ambitious to me but I guess it's pretty heavy).
If you are at B2 level already, you can take the Upper French Studies Programme which is 453 hours and costs 2718 €. This course takes you right up to C2 level which means you are pretty much fluent!