Attack the Center Squares. Develop Your Minor Pieces (Knights before Bishops) Don't Move Your Queen Too Early. Castle and Move Your King From the Center. Don't Move the Same Piece Twice. Bonus Principle: Have a Plan
I've seen lists like this with 200 rules. This keeps it simpler. (I would clarify 5: "Don't move the same piece twice in the opening, although all of these tips here seem to be opening principles, so it's probably implied.)
Attack the Center Squares.
Develop Your Minor Pieces (Knights before Bishops)
Don't Move Your Queen Too Early.
Castle and Move Your King From the Center.
Don't Move the Same Piece Twice.
Bonus Principle: Have a Plan