The indicator light on the connector tells you about the charging state. Amber/yellow means that the battery is charging. Green means charging is complete.
AFAIK, it's not possible to over-charge the battery. You should be OK with leaving the Macbook Pro unattended with the power adapter attached.
Thanks for your reply! I also have another quesion about the battery. When I first got the laptop, I made sure I charged the laptop and then drained it fully about 3, 4 times. Am I now ok to charge it if its half drained if I need to or will that train the battery for the bad?