The iSight camera had died but because the Macbook was five years old, the Apple store won't do repairs on it. However, they gave me names of repair shops that might. Instead, I bought the replacement camera and spudger from iSight and used some of their instructions for the replacement (my exact model was not represented).
The repair was successful and it once again allows me to Skype with the family when on business travel.
The instructions for replacing an iSight camera involve doing a lot of steps that don't have anything to do with gaining access to camera. I removed the battery, removed the display bezel and removed the screws holding the display to get access to the back side screws for the iSight camera. The only tricky part is the clips that hold the screen bezel on (the border around the screen). When you use the spudger to pry away the bezel from the screen, the gray plastic clips tend to stay with the bezel (about 75% of them). You need to remove them from the bezel and put them back into their case poistions before trying to snap the bezel back into place otherwise you can't get the bezel back into place.