Settings that have been best for me (Nikon D3) at MK, Epcot, and at
Disneyland have been:
Tripod, camera on Manual
ISO 200
Shutter ~20 sec.
Aperture - Anywhere between 16-22, depending on the scene at hand.
I typically use a 24-70 f2.8 lens.
Now... Every camera is different, so depending on your model, you'll have to adjust a bit here and there. It's not gospel what I just posted, but it's an adequate starting point.
Illuminations is harder to shoot simply because there are points of LOTS of darkness throughout the show and points of LOTS of light during the show. And it's nearly impossible to get a great reading until the show begins.... but then you don't want to spend the entire show messing with settings and not seeing the actual show with your eyes. So play around with it a bit, but make sure you don't stress too much about it!
The MK and Disneyland fireworks are MUCH easier to gauge. You'll want to take a good meter reading on the castle when it is lit at it's absolutely brightest before the show. Make sure you have a nice long shutter (anywhere between 10-30 seconds) and then adjust your aperture so that the castle isn't blown out. For my camera, blue is the hardest, and it's always the color channel I blow, so I always make sure, prior to the show, that I get a solid meter reading on that color. I have another camera body that blows the red channel easily... so sometimes it is just about the model you are shooting with.
Good luck! Shooting fireworks is REALLY fun. Always a plus on any trip for me.
ETA: All this advice was for fireworks. I just re-read your post and realized that you were asking about parades as well.
For a novice I would suggest putting your camera in Av mode with auto ISO. It will do a fairly good job if you have a fast lens (f1.4, f1.8, f2.8 or f.3.2). There are a few tweaks that make it even better, but I don't want to bog you down too much, and most of the cameras will be sufficient.