Get your pieces out into the centre quickly. The opening is a race to see who can get their pieces out first while keeping at least a share of control of the centre.
This is the main point to remember; all the other rules are just footnotes to this one
More detail on winning the race:
Move pieces not pawns, and
move them to their best squares in one move if you can, and also
try to gain time if you can by aggressive moves.
Move minor pieces out first, not your Q or RRs which can be attacked and lose time
Get a firm foothold in the centre and don't give it up
Generally move Knights straightaway to f3/c3 or f6/c6
Move your king to safety at the side by castling King's-side (which also gets your Rook into play)
Complete your developmentbefore moving a piece twice or starting an attack
Keep your queen safe
Don't grab pawns or attack if you haven't completed development
What to do if there is a lead in development:
If you are ahead in development, start something going and open up lines for your better pieces
If you are behind in development, don't start anything and keep things closed until you have caught up
Lasker's rules for the opening
Do not move any pawns in the opening of a game but the King and Queen pawns.
Do not move any piece twice in the opening, but put it at once on the right square.
Bring out your knights before developing your bishops, especially the Queen's Bishop.
Do not pin the adverse King Knight (ie. by Bg5) before your opponent has castled.
Why should you move the knights first? Well, knights are very much more effective if they are in the centre. (Bishops are more effective here too, but they can work from a distance). For the opening that has to mean Knights moving to c3 and f3 (or c6 and g6). Where should the Bishops go? The White King's Bishop on f1 could go to b5,c4,d3 or even e2. Which is best? That depends on what your opponent is up to. So, move your knights straight away to the centre, and while you are doing that your opponent's moves may suggest to you where you should put your bishops.
Fine's rules for the opening
Open with either the e-pawn or the d-pawn.
Wherever possible, make a good developing move which threatens something or adds to the pressure on the centre.
Develop knights before bishops.
Pick the most suitable square for a piece and develop it there once and for all.
Make one or two pawn moves in the opening, not more.
Do not bring your queen out too early.
Castle as soon as possible, preferably on the king's side.
Play to get control of the centre.
Always try to maintain at least one pawn in the centre.
Do not sacrifice without a clear and adequate reason, eg.:
it secures a tangible advantage in development
it deflects the opponent's queen
it prevents the opponent from castling
it enables a strong attack to be developed
Nimzovitch's Seven Axioms
(from My System)
Development is to be understood as the strategic advance of the troops toward the frontier line (the line between the fourth and fifth ranks).
A pawn move must not in itself be regarded as a devloping move, but merely as an aid to development.
To be ahead in development is the ideal to be aimed for.
Exchange with resulting gain of tempo.
Liquidation, with consequent development or disembarrassment.
The pawn centre must be mobile.
There is no time for pawn hunting in the opening, except for centre pawns.
Lasker's rules for the opening
Why should you move the knights first? Well, knights are very much more effective if they are in the centre. (Bishops are more effective here too, but they can work from a distance). For the opening that has to mean Knights moving to c3 and f3 (or c6 and g6). Where should the Bishops go? The White King's Bishop on f1 could go to b5,c4,d3 or even e2. Which is best? That depends on what your opponent is up to. So, move your knights straight away to the centre, and while you are doing that your opponent's moves may suggest to you where you should put your bishops.
Fine's rules for the opening
Nimzovitch's Seven Axioms
(from My System)