Thoughts going through your head...

Other than "best possible move," what are some key things I should be considering after getting towards the late mid-game/early end-game?  Formation? Gaining material? Pushing passed pawns? Any kind of insight on how I should be analyzing my next move would be appreciated.

Well to be good at endgame you need to know some very key, basic positions, ideas, and principles. Thus, when you are entering into an endgame, you can be thinking about how you can steer the game into a position you know how to win or draw, or how you can use an idea or principle to gain an edge on your opponent.

Tempo.

Golden rules I follow:

1) Look into every check and capture. This will minimize your oversights.

2) Consider every move, including an apparently wrong move. Consider all opponent's reply to those moves (most people cannot do that if they are running gazzilions of simultaneous games - playing more simultaneous games than you can handle will invariably lower your quality in the games).

3) Look for possibility of a pin, skewer, fork, discovered attack, removing the guard and mating patterns.

4) Control of the center with pawns and pieces.

5) Maintaining a good pawn chain, avoiding doubled pawns, possiblity of getting a passed pawn; preventing or hampering opponent from doing the same.

6) Advancing pawns where practicable.

7) Finding weakness in opponent's position and increasing pressure on it by amassing forces.

8) As The_Pitts has said, prefer moves which gain a tempo (opponent has to waste a move to counteract).

9) Avoid speculative sacrifices (most beginners inspired by games of the great masters falsely thinks that sacrifices wins games - not! The great masters make precise calculations before making a sacrifice - if you cannot calculate that far, do not sacrifice). I have seen several of my opponent lose just because of this tendency.

Always look for double-jumps.

The 'key' idea in chess is to kill the opponents king. All of your thoughts should revolve around that. To kill the king, you must attack him with more force than he has defending him. In order for that to happen, you must create this imbalance in force. There are many different ways of making this happen, many different techniques. When we study chess, we learn common tactical weapons, common development schemes, common piece manuevers, etc. The trick for each and every single one of us is applying those ideas, applying chess theory, to the board situation we are facing. To me, the 'key' is studying the fundamentals until they are really engrained. Then you will have many more ideas to draw from when you are playing. It will be like coming across an old friend when you see that you can apply a certain technique to the position you are facing.

Would it a better to play games or constantly solve pouzzles to increase my tactical planning and board vision?

solving puzzles is more effective in developing tactical sense, but then you do not get to develop sense of strategy or planning, which is essential in a full game.

So what's the most widely accepted way of improving your chess game, just playing game after game? Doing tactical puzzles?

looking over grandmaster games.

Some people are of the opinion that playng simultaneous games help to improve your  playing. Well, it gives experience and game "sense". But do not exceed your capacity! It is far better to play a single game and to think deeply (several ply, every check and capture, every possibility - which I do!) than to play multiple games and spend only a few minutes on each. Also it does not pay to have your brain fatigued - then it is all downhill and you will become frustrated.

Summary: optimum quantity (of games, problem solving and studying books on endings, middlegame and openings, in that order) without sacrificing quality.

learn the lolli attack!!!

Actually create an opening repoitoire so you won't make mistakes in the opening.(This is what my coach says)

I am a beginner in chess game. I mean how to move the pieces but donot know any strategy or game planning. I used to play with commonsence according to circumstance. But now I started reading and practicing  "Know your first move." by Russian Grand master Sokolsky. I feel that it's very systematic and teaching. Now I can see that my game is improve. Most important is to practice and trying to apply what you read.

As someone said you need to know what a good position is in the endgame.  Learn what a good position (or won) is and even if you have to drop material to get there sometimes it is best to do it.  Then you have reached a point where you know how to win.  \

Basically chess is about finding the key to the position.  The more positions you know the better you will be at finding the right move. 

not necessarily true.  You need to look at the right continuations, not just a ton of wrong ones.

 All valid points however you still have to know when to break each of these rules....

Eg...doubled pawns can be a great advantage in the endgame(if they are the only ones on the board and neither can be taken then it is an automatic win.)