Rule of Thirds
Amongst the myraid of information on the internet (including this one), there's only one composition methology that impacts greatly to getting that great photo. The first one that makes a big difference is the "Rule of thirds". By using this "rule", it will improve any photo in any situation.
The basic premise of this rule is that a photo is divided into thirds and the aim is to place the object of focus in 4 intersecting spots. So in simple terms, don't put the object you're photographing in the middle of the photo.Whilst it's called the "Rule of Thirds", it is like a road rule, it's meant to be broken so don't follow this to the letter of the law. Creativity occurs when the rules are broken.
Check your background
The other tip I can provide is to look out in the background of offending objects. Below is a classic example of a photographer not doing their job. In the foreground, we have a car which obviously is what the photographer is taking a photo of for a news article, however in the background, the photographer has failed to notice the "Wrong way go back" sign (albeit blurred).
It may be an oversight from the photographer but if someone wants to communicate a hidden message, this is certainly one way.

Take more photos
The last piece of advice I'd give to choosing the right camera is to use it and use it often. There's nothing worse than seeing people buy a nice camera and end up gathering dust after the honeymoon period.

