Here's what you should do Adam.
1. Create a separate facebook account just for work.
2. Take professional picture of yourself and make it the main photo. Take a picture of the dealership and use it as the header picture.
3. Everyone you meet (sold or unsold) gets a facebook friend invite. Make sure you get full names and e-mails, this will make inviting people easier. Then you send them a message like this on facebook:
"(Customer Name), It was a pleasure meeting you today at (dealership name). I wanted to thank you for taking the time to stop in. I noticed you are on facebook so I thought I would send you an invitation to connect. I know you have a lot of choices when it comes to purchasing an automobile and I hope to earn your business by providing you with excellent service before and after the sale. If there is anything I can ever do, please do let me know how I can help." Sincerely, Adam"
My message would be a little different if I sold them on the first visit.
4. Every time you sell a vehicle, ask people if it would be okay to take a picture of them to post to your facebook wall of happy customers. Then ask if it's okay to tag them in the photo. Most people will be cool with this since they like to show off their new car. And you posting the picture makes them seem less vain. Those who are well spoken should be shot in a promotional video that is posted to your YouTube account and then shared on facebook.
5. Wish everyone a happy birthday each day on facebook.
6. Once a week make a walk around video of your favorite used car and post the video on facebook. Write a message that asks your friends to share the video so we can find this car a happy home.
7. Get with your service manager and post a service special on your wall occasionally.
8. Use the events feature to invite people to sales or new model intorductions.
9. Look for opportunities to engage with customers when they post something. People like when other people comment on something they posted or wrote. This is your opportunity to win them over as a friend.
10. Use the chat feature to make contact if you can't reach somebody by phone.
11. When befriending a new potential customer, look for mutual friends, this will help you build instant rapport with somebody. As your following grows, this will happen more often.
12. Don't let it become a distraction, spend your time on facebook wisely.
Side Note: Managers, consider having salespeople create a facebook account that is controlled by the dealership. Tie it to the work e-mail, this way if an employee leaves the dealership they won't be able to take their customers with them to another dealership.
Hope that gives you some insight as to how to properly use facebook. Consider facebook as a social CRM tool. This will really help you build a customer base that won't forget your name.