My inside rearview mirror came loose today, how do I get the old glue off the glass and what do I use to get it to remain on the glass.

1991 Pontiac Sunbird 1.8L, 81,000 miles. My inside rearview mirror came loose today. The thumbnail size glue patch is all that remains on the glass and some glue residue is on the mirror arm (I would think that I would need to scrape that off). I had a friend who had this occur in her Jeep Cherokee and she went through a lot to get it to stay up. I know super glue does not work. Therefore, I must ask-how do I get the old glue off the glass, and what do I use to get it to remain on the glass forever?