Beginner Basics
As far as improvement goes, there are a lot of ways to get better at chess - lessons, reviewing annotated master games, chess trainers, studying databases, etc.
You can survive the opening with basic opening principles - influence or occupy the center, develop your pieces quickly, don't move a piece more than once in the opening, castle early, develop knights before bishops, etc. Just about every player has heard them.
But what's a player to do after the opening?
I think that if a chess player strictly follows the basic fundamentals of chess, that player can reach an expert rating by studying only one thing: tactics. And playing a lot of chess games, of course. Play as much as you can or as often as you feel like.
These fundamentals must be factored into every decision/move, then followed & executed.
At EVERY move - consider how the following basic fundamental elements factor in (They are NOT in order of importance) -
* Think defense first (ask yourself, "what is my opponent's idea?" and unless you've got a better thing to do, stop your opponent's idea.)
* Pawn Structure (keep the fewest 'pawn islands' and keep 'pawn chains' instead of doubled pawns. Also, know the value of each pawn - the two center pawns are a full value of 1.00 and as it progresses towards the side of the board, the pawn value decreases by .10. I.E. the bishop pawns on the 'c' & 'f' files are valued at .90 and the knight pawns on the 'b' & 'g' files are worth .80) Center pawns are worth much more than the others.
* Material (knowing piece value & how the values can sometimes change)
* Space (the amount of squares you control or occupy)
* Development (getting knights, bishops, etc out as soon as possible & not moving a piece more than once in the opening or until they're all developed. Also knowing that rooks belong on open & semi-open files & place pieces where they are most mobile)
* King Safety/Castling Early
* Time/Initiative (dictating play or forcing your opponent to react to your moves)
* Control of the center (the center is where knights, bishops, queens, & rooks have the most scope)
There are more advanced elements but these are the most basic to learn, employ, & execute to start winning chess games consistently.
All of these basic fundamental elements of chess are EXTREMELY important and aside from obvious blunders, they are the primary reasons games are won or lost. Really - in assessing each of your losses, you can attribute the reason to any one or more of these elements if it wasn't because of an obvious blunder of material. I.E. - "I let my opponent take the initiative" or "my opponent beat me in development & I couldn't recover" or "material was even but my opponent's pawn structure was superior to mine".
When I struggle to find a good move, the main thing I try to make certain of is that I don't make my position any worse. When the game is close & complicated, stay strong & consider any move - just don't make your position worse. That way, when your opponent makes a mistake that allows a tactical shot, you're in a position to pounce & perhaps even knock him out with a tactic you've studied, seen, or learned from a tactic database, book, previous game, or another source.
For a beginning player, considering these elements at every move & learning basic tactics & combinations is guaranteed to put a few more games in the 'WIN' column. Of course there's always more, like basic checkmates and endgames, but that, in a nutshell is what helped me progress into the USCF ‘Class A’ competition.