First you need an invitation letter from CERN where they "invite" you to come to work there (for a year, in my case). I requested it at the beginning of June. CERN sent that letter to the French, who then forwarded it to their consulate in New York. The consulate then sent me a letter in mid-July (6 weeks later!) asking me to come to Manhattan to apply for the visa in person. Luckily, I had already made an appointment at the consulate and showed up on July 21st to submit my application. That was an experience in itself. They are very strict -- you can only show up for your appointment time, and if you are late or don't have an appointment, forget about it. The French consulate visa section is in a swanky neighborhood on the upper East side near Central Park, and as I stood in line to go in I realized that I was surrounded by college-age girls wanting to study abroad for fall semester. The passerby were quite amusing, because they scrutinized the line curiously, wondering why we were lined up at noon on 74th street in 90-degree weather... I half-expected them to jump in line too! They looked disappointed as they read the sign on the building and saw that we weren't getting concert tickets -- just a visa to live in France.
Once I got in the building I waited for ~45 minutes to see the cashier and be fingerprinted. The nice thing about other countries is that a scientist visa is usally free! Then I waited another 90 minutes to be called up to a window, where they ask you such questions as "Do you know any French?". I nervously replied "un peu, but I am learning" and they said they would call me in 2-3 weeks. Over a month later, I finally received my reply! I still need to go back to the consulate so they can physically stick the visa in my passport, but this definitely makes it seem like I'm on the home stretch. 2 weeks to go!