Well different people do it different ways, I'm sure you've seen enough of my photography. I have been photographing reptiles in the wild for a couple of years now for both science and for fun and over that time the amount I've learnt about this amazing art is enormous, experience and being out there taking pictures with other people is absolutely the best method of learning.
I say my style comes from my understanding of the animals in nature. That is I try and capture them as naturally as possible, and in this way there are lots of pictures out there other people toat as amazing I just don't like because to me they don't look natural. (Of course I'm more applying this to wild animals). That's just how much personal style influences not only your own pictures but your perceptions of others.
So from my experience there's not much advice I can really give other than to find yourself a personal style you really enjoy (preferably one I like too
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) and that experience is the best teacher. I will however give some brief advice about gear and technique.
Gear: You can take pictures on anything from your Iphone to a professional DSLR, it doesn't matter brilliance in a picture isn't all about how many pixels it has. If you're looking to take nice photos that you can print and display in your room or house I'd recommend at least a high level point and shoot (Olympus XZ-1 just being an example). But you're probably better off using a low level DSLR, Nikon are easier to use, Canon are slightly higher quality, it really doesn't matter what you choose unless you want to get serious, watch out for Olympus they make some amazing lenses they have a serious chance to rock the market in future. It's important that you actually learn how to utilize the setting on these camera ESPECIALLY THE POINT AND SHOOT, there are so many functions, buttons and settings it can get confusing but read the damn manual and know how to do what you want, use manual,
learn how to manually set the flash, etc. There's no reason you shouldn't be able to take great pictures with lower level gear if you use it properly (it all comes back to experience).
Once you've decided on a Camera and lens, (plenty of threads on advice for lenses) the next big thing is the flash. Never ever underestimate the power of a good flash to make a picture. Flashes can wipe out shadows, light up the background, bring out colours of an animal (I find these colours are usually fairly near true but I've seen green snakes turned blue by flash before). A flash setup can be useful both day and night. Again different people use different things that work for them and you'll need experience to figure out what works best but even the cheapest range of flashes or the onboard flash can improve your pictures if you use them right.
Technique: Get low with the animal, next to the animal, slightly below the animal, just try not to be looking down on the animal if you don't have to be. Especially for shots that you want to look more dramatic or impressive.