Hi, along with a few others here, my main advice is practice, practice, practice. And enjoy yourself along the way...
I've been a professional photographer all my working life (10yrs now) and was a very keen photographer for most of my teenage years - I can happily say I am still learning new things. Keeps the job interesting as they say!
Photography has a lot of technical elements (exposure, timing, photoshop/darkroom printing, lighting, composition, colour): become proficient in these and getting the results you want will be a lot easier.
Know what you wish to convey with your photographs. Other posts have mentioned trying to get a message into your photos - a feeling of intimacy and tenderness between a mother and her new baby for example. The sublime beauty of a landscape. A sense of drama in an action photo etc. This is where knowing your technical stuff really helps as this can help convey your message in choice of lens, exposure, lighting and so forth. But the message then adds the extra bit of 'zing' that will help make the photo stand out from the crowd.
Photoshop is a wonderful tool and is one which I feel is there to be embraced. One word of caution; although a lot of things can be fixed with it, it is often quicker and easier to get things right as much possible in the camera first!
Someone else mentioned studying all forms of art, and I agree with this. What works compositionally is the same be it an oil painting, pencil sketch or a photo. Play with lines of sight (not necessarily actual lines - it can be a look between two people) to keep the eye moving around the photo and the viewer interested, but then using the composition to keep the eye within the frame. There are some rules on composition and they do generally work well, but there is never any harm in pushing the boundaries...
http://www.nationalgallery.org.uk/c...ectionPublisher.woa/wa/work?workNumber=NG6301
Notice how lines at the corners bring the eye back into the frame - the line of the field, the dog looking up at the owner, the clouds and tree bringing us back in at the top. Then the eye, once back in the middle is drawn back to the blue of the ladies' dress and back to our main subjects again.
A couple of points on portraiture: we instinctively look at the eyes of the subject first and then we pay attention to the subject's expression. Pay heed to these two points and you can often get away with murder 'technically'!
Having read over this I apologise for going on for so long - I think I may have got carried away.
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Anyway, I hope this has been of some help (I could probably continue for a fair while longer) and that you continue to enjoy your photography for a long while to come.