Hey Pamela, I've had some success with putting my hood on the front of the lens and actually placing the lens right up against the glass. This will get rid of any reflections and reduce fingerprints.
ANother trick that you have to do since you wont be able to use flash is to bump up your ISO which will give you better shutter speed in the low light conditions
Some cameras really get grainy with high ISO's so this will be something you will have to play with to see which number is the right setting for you.
Got this while at the Detroit Zoo a few days ago with a Canon 5D that I had placed right up to the glass. I bumped the ISO up to 800 which helped. Like you said, with shooting digital, I was able to take a few with diffrerent settings and see which ones were giving me what I was going after till I finally liked the 800ISO
As for the Polar Bears in my other post, all of those were taken through very thick glass, but I figured out a way to get rid of the nasty shadows or reflections by again putting the lens right up against the glass or standing far back from it.
Hope that helps and good luck with your shots