Great thread Christina,
I certainly support many of the ideas suggested above (and, no doubt, below this post)
OK let's see if I can come up with some different/expanded ones, perhaps not what I'd consider the most important for a beginner (they're already well covered above), but those necessary for the 'ultimate success':
1) Research your subject - learn how it behaves, this can be applied to more than just animals (and I include humans here) or other moving objects, think how light reflects and/or refracts from the surface of your subject - and background! This knowledge, when applied to moving things, will give you a better chance of predicting what's about to happen, so you can get the shot.
2) Timing/positioning can be important - This is really all about 'the light', but I'll give two examples;
a) when you arrive at a new location, by all means take a shot, but also think about whether, an hour or more later, the sun may be in a better position to illuminate the subject* (typically a building, sculpture, landscape, etc.), if you've already missed the best time of day, return earlier next time.
* the sun moves 15 degrees per hour, so 2 hours = 30 degrees, 3 = 45, etc.
b) if photographing a staged event, say; a bird of prey, or aircraft, flight display, get there early enough to position yourself so that you are not shooting into the sunlight (or at least, as little as possible) - unless that's what you want!
3) Don't get overwhelmed (perhaps this one is more for beginners, but also when moving outside your 'comfort zone') - there's a lot to learn (and you should learn it), but you can't expect to learn it all at once, in fact the plain truth is; you'll never know it all, you'll always be learning better ways to do things. So tackle one bit at a time, get that gripped and move on to the next topic.
If books/reading doesn't suit you, try something else; video tutorials or face-to-face at a camera club, in a classroom, or even with personal tuition.
Above all; practice and experiment (a lot).
Cheers (and have fun all),