I used a manual setting for the fireworks and night pics, and a combo of auto and manual for the day time shots. It kind of depended on how long I had to take the shot, I didn't want to be in the way too much. That's a whole other thread!
I did not use a tripod. I just did my best to steady on a nearby trashcan, or the handle of my stroller.
Good luck with your digital. The best part about digital is that you can really play around with it at no extra expense. Take a million pics...trash the ones that don't come out, but you'll get a few great ones too! I love my FinePix. My poor old Nikkon SLR is sitting in the closet now, gathering dust