WHATCH YOUR DEPTH OF FIELD - Choose your focus point to maximise the Effects of D.O.F.
EXPERIMENT TO FIND OUT HOW HIGH YOU CAN GO WITH YOUR ISO 400/800 ect and still have acceptable (to you) results
Learn to hold your camera firmly to minimise movemen
If you have a macro resist the temptation to go too close, pull back a little and crop on the computor
If you have a standard lens, put it to minimum focus and move yourself
Put your lens in manual focus, set it to roughly the size you intend to photograph and move in and out
When approaching a live subject, put up your camera and look through it as you approach: approach slowly: take shots as you come in - then you will have something even if it flies/moves away
Watch the background to see if you can find a less cluttered one but a bright (small) subject against a dark background requires you to put your exposure on manual (and test it) or your subject will be over exposed.
The more you can learn about your subjects the more you will recognize significant behaviour.
Behaviour (action) of some sort is better than static (portraits)
If you have the ability, try for art / artistic results.
Try different shutter speeds, see 11 above
Find your local 'patch' and use it to practise, learn your camera. When you find a unique opportunity, its TOO LATE to practise !!