This is a great topic, with great advice given already.
My contribution will be-
1. Developing a plan (for attack and defense).
2. Understanding why a move was played, not just memorize them.
3. Timing and sequence of moves are important.
4. Identifying weak squares for both players.
For beginners, I would suggest FORGET about openings. They are a waste of time for you at first. You don't start out learning math by taking calculus, or to play piano by tackling Chopin concertos. You need to learn the basics well before proceeding to the more complex areas of the game.
To wit, the rules in post #9 are a good start, but I would add:
Develop Knights before Bishops - as a short range piece, they need to advance early - and Bishops before your Queen and Rooks. These minor pieces find good squares early more easily, and getting them out clears the back rank for castling and eventually connecting Rooks.
Try not to move a piece twice before the others are developed once. You will only rarely be able to get them all out before one must be moved again, but this is the goal.
The Chernev book recommended in post #13 is excellent. Also, after that, Fine's Chess the Easy Way.
I do all those things but my games still turn to crap fast.