I have just registered a car here (though I bought it used in Switzerland). The steps were as follows:
1. Get insurance. You can use
www.comparis.ch to get quotes but when you go to the car registration office they will need to have a record that you have insurance. This record is transmitted to them electronically.
2. Fill out the Demande d'Immatriculation. Attached is a link that you can fill out on line and then print.
http://www.san.vd.ch/documents/0211_070223_000.pdf
You'll need to check which shape of number plate you need for the back of the car. You can get a square one or a long thin rectangular shape according to the make of the car.
3. Go to one of the offices with the original ownership document of the car, the completed "Demande d'Immatriculation" and a copy of your work permit as well as your passport. My permit was not yet issued so I took an "attestation" from my employer that the application was made. The various addresses for the offices where they issue the registration are printed on this form. I went to Lausanne and it took about one hour. I did not need to have the car checked but that might be the case fo you because the car was not originally registered here. If so, they will apparently give you an appointment for a later date when you'll need to go back for the inspection.
4. They give you the plates there and then and hand you a printed car registration document (a grey form). Make a copy of the grey form and keep it in case the original is lost or stolen. Keep the original in the glove box of the car.
About a week later you'll get a bill in the mail. I had to pay about CHF375 for half a year (Peugeot 207).
Good luck.