Opening System for White

The King’s Indian Attack is more an opening system then an opening per se, it involves the moves 1. e4, 2. f3, 3. d3, 4. g3, 5. g2, 6. bd2, and 7. 0-0 (although, as you will see later, I'm going to recommend a different move order starting with 1. ♘f3 below). It can be played against any opening move that black makes, except one, the Scandinavian, which I will address below. What this means for you is not having to learn all the different openings and their myriad variations.
King's Indian Attack formation

Here is a game, A Night In Tunisia , played by Bobby Fisher that illustrates some of the possibilities of this system. One of the interesting aspects of this game is that Myagmarsuren playing Black does everything right, does not make any bad moves, but still loses to Fisher. View a video tutorial of the KIA.

The one exception is if black plays 1...d5, the Scandinavian Defence (also called the Center Counter Defence). You have two options, either go into the main line which is 2. e4 x d5, or play 2. ♘c3 defending the pawn. You do not want to force a KIA by playing 2. d3 because Black can just take the e pawn 2...d5xe4 and after you take back 3. d3xe4 Black can play Queen takes Queen 3...♛x♕d1 and Black has more than equalized because White has lost its first move initiative after 4. ♔x♛ Black can develop one of its pieces giving it the initiative View . On 2. ♘c3 Black can either take on e4 or push the pawn to d4 attacking the Knight.

Okay, now that I've just taken you through the classic King’s Indian Attack move order with 1. e4, I'd like to recommend another move order, which can reach the same KIA formation, starting with 1. f3 and followed by g3, g2, 0-0, d3, bd2, and e4, call it the Réti King’s Indian Attack (it also avoids having to study the Scandinavian, because now if Black plays d5xe4 you can just take back d3xe4 and you now have an open file for your Queen's Rook). The advantage of 1. f3 is its flexibility, it can easily transpose into any number of openings. This allows you to wait and see what Black does before committing to a particular plan, although I would recommend sticking with KIA plan as it limits Black's responses. Note: The most common reply by Black to 1. f3 will be 1...f6 (Black openings often start by mirroring White's first move). Other popular replies are 1...d5 and 1...c5, in that order.

And now for something entirely different: 1. d4

I'm not going to go into this opening move for White too deeply but it would be remiss of me to not mention it. Queen’s pawn games tend to be more closed, more strategic, less tactical then Kings’s pawn openings, in other words, they are slower to develop. Unlike the King's pawn, the Queen's pawn does not immediately expose the King, and unlike the King's pawn, which is not protected, the Queen's pawn is protected by the Queen.

If this is something you might prefer then I would suggest the London System. Like the KIA, it is an opening system so there really isn't a lot of opening theory to learn. It begins with the moves 1. d4, 2. f3 and 3. f4...

8/8/8/8/3P1B2/5N2/PPP1PPPP/RN1QKB1R w - - 0 1

with an eventual c3, Nbd2, e3, and Bd3 (notice that the dark squared Bishop is outside the pawn chain, this is not case in most other Queen's Pawn games)...

8/8/8/8/3P1B2/2PBPN2/PP1N1PPP/R2QK2R w - - 0 1

Note: Although 2. Nf3 is given as White's second move in most books about the London System, it is now considered more precise to play 2. Bf4 before Nf3. See a review of the book Win With The London System that explains this move order, known as the Neo-London.

Opening System for Black

As with White you want to try and play your King's Knight out first 1...♞f6, but if White plays 1. e4 then in order to play your King's Knight you have to first play 1...d6 otherwise White can push the pawn to e5 attacking your Knight. On 1. d4 you can play 1...♞f6 immediately. You're aiming for the moves ...d6, ...♞f6, ...g6, ...♝g7, and ...0-0.

You basically want to achieve a formation like this...
Black formation
And depending on what White plays, followed by ...c5 (and rarely, very rarely ...e5, you do not want to block your black Bishop) and then either ...♞bd7 or ...♞c6. You'll notice that your pawns are mostly on dark squares giving your light squared Bishop a lot of breathing room. Because the Queen's Bishop has so many possibilities in this kind of formation it is almost always the last minor piece to be developed.

Below are some examples of black openings that use this formation...

Against 1. e4 or 1. ♘f3 the Pirc Defence (pronounced “peerts”, although, most people, as the guy in video, pronounce it “perk”)