It usually only takes 5-10 seconds for the shot to take effect. This is normal procedure. After this, the heart stops beating. There might be some final respirations (breaths) as the body catches up but it does not take long for the pet to pass away. This is a very peaceful procedure and the dog feels no pain.
I am very sorry that you have gone through this. If you are not familiar with the story of the rainbow bridge, you might take some comfort in it.
http://www.petloss.com/poems/maingrp/rainbowb.htm
You can read more about euthanasia here:
http://www.thepetcenter.com/imtop/euthanasia.htm
Let me know if you still have questions.
