Long and the short of it is to just learn your camera. Learn how it functions, learn how long the delay or lag is in the shutter. Learn how all the settings work.
Also, the best beginner book out there is The
National Geographic Field Guide for Photography.
Watch your compsitions - look for that stray tree branch that you didnt see or those phone wires or trash cans. Don be afraid to move your feet and take 3 steps in any direction - or duck down - to make your photos better. I love sillouettes, i love things framed well. I like good composed shots, reflections, etc.
Nightttime - You dont necessarily need a cumbersome tripod. There are plenty of level surfaces handy - Railings, trash cans, chairs, benches. All sorts of things you can set the camera on and use it and get the same long exposure night shots..... Unless you want fireworks.
Fireworks, fireworks, fireworks......
Where do i start? Depends on the end result that you want, really. If you want the multiple burst, streak shot where it looks like 4 or 5 airbursts are going off over the castle, youre going to want a tripod, ISO 100 and f/11-f/16 and end up with a 20sec ish exposure, depending on how much of the show youre trying to capture.
On the other hand, if you just want to capture that one burst or that face from over the castle, ISO 800, f/2.8 and 1/125th of a second.
In a nutshell, just learn your camera and work on basic composition and proper exposure. Which for Bright Daylight, the sunny f/16 rule applies. If your subject is in bright daylight, your exposure is 1/ISO speed and f/16. so at ISO 100, the expsoure is 1/100 at f/16 or 1/500 at f/8.