Your first question before making almost any move is whether there is a tactical opportunity for you on the board. If there isn't—as routinely will be true—then your choice of move will be determined by strategic considerations: attempts to secure positional advantages that may ripen into tactical opportunities. One goal of strategic play is to create the types of positions where tactics, such as the double attacks we have studied, become possible. It is not the purpose of this site to advise you on effective strategy in any depth, but here are a few elementary points on the subject, particularly as it relates to the knight.
A couple of general things first. It often has been observed that good positional play leads naturally—perhaps even mysteriously—to chances for tactical wizardry. Why? The reasons have to do with what good positional play accomplishes. The most important purpose of it is to expand the power and mobility of your pieces—often the same thing, because the power of a piece largely is a function of how many squares it attacks, which in turn will depend on its mobility. A rook on an open file—i.e., a file containing no pawns—is very mobile and for that reason very powerful. Likewise a bishop on an open diagonal. So when you look at a piece and assess the quality of its position, consider how many squares it controls. A fully deployed army of pieces will attack a large share of the squares on the board, especially including squares in your opponent’s half of the board, many of them two or three times. A second purpose of positional play, of course, is the converse: limiting the power and mobility of your opponent’s pieces. The fewer the squares he attacks, the greater your ability to put your own pieces there.
These principles relate to tactics in obvious ways. If your pieces have lots of room to move and attack lots of squares, that means they can range more boldly into parts of the board where they might cause trouble to your opponent; it also means you are more likely to be able to coordinate them, bringing two or three or four pieces to bear on a sector in ways that permit a combination: perhaps sacrificing one, pinning with the other, and then capturing or forking with the third. Note that an individual piece does not threaten much when it ranges into enemy territory by itself; as we have seen many times, a knight usually needs help from other pieces to set up a good fork. Meanwhile if your opponent’s pieces are constricted or blocked in their movements, this does more than prevent them from causing you trouble. It makes them prey to tactical strikes, because they give your opponent fewer good options in responding to checks, captures, and threats that you make.
So when you aren’t playing tactics, think about these two considerations: how you can place your pieces to enlarge the amount of territory (“space”) they attack and control; and how you can place your pieces and pawns to confine your opponent’s army. This partly is a matter of simple gestures like moving your rooks onto open files, getting your knights and bishops off the back rank and out where they can exert pressure down the board, and keeping a pawn or two in the center so that your opponent can’t plant pieces there and so that your pieces there are protected. It’s also a matter of subtler things: exchanging pawns where the exchange will create an open or half-open file for your rook (but perhaps not if it creates such files for his rook); placing your pawns (and keeping his pawns) on squares that block the paths of his bishops; and thinking about how pawn moves and exchanges affect the lines open to other pieces on both sides. These are general ideas to consider when you are picking a move without any immediate tactical purpose.
Against this backdrop consider the knight in particular. The knight doesn't need open lines because it jumps rather than slides. But it still needs help from your pawns to be effective. The first thing to grasp is that the knight’s prospects for creating mischief tend to increase as it moves up the board. A White knight on f3 early in the game serves mostly a defensive purpose, and a valuable one (though of course even this knight has offensive potential, as we occasionally have seen); the same knight on, say, d4, d5, or d6 becomes a terrible offensive threat. On d6 it strikes out at eight squares, including six in your opponent’s half of the board; from any of the squares just listed the knight can attack the opponent’s back rank, and often his king, in one move. (More than 90% of the knight forks we have considered involved the king as one of the two targets.) So an important general strategic aim is to get one of your knights planted on a square on your fourth rank or beyond. An especially good place to plant a knight is on a square near the center, since from there it can make threats and influence play in all sectors of the board. This is why chess books often speak of the importance of controlling the center, and of the battles that players wage to keep a pawn on the central squares and to keep enemy pawns away from there. The point is not necessarily that pawns in the center themselves threaten anything; it is that the pawns control the squares that they can attack. When you have a pawn on e4 it controls not e4 but d5 and f5. Enemy pieces are unable to move to those squares; your pieces can. Having good central squares on which you can plant your pieces is important. That is where they are most powerful.
The key word is “plant.” It’s not much use to move your knight to a central square only to have it chased away by a pawn. You have to create a hospitable square—an “outpost square”—for your knight. A good outpost (d5 in the diagram on the left) is a square where the knight cannot be harassed by pawns, because the enemy pawns on either side of its file are gone, are blocked, or have advanced up to your knight’s rank or beyond it. Ideally the well-posted knight also is protected by one of your own pawns; that will prevent it from being chased away by one of your opponent’s rooks or his queen. The remaining point is to make sure the knight is not threatened by one of your opponent’s bishops or knights. The White knight in the diagram to the left has all of the good properties just described. It is planted in the center of the board on d5, where it has two ways to check the Black king. So long as the knight stays where it is it will be a constant forking threat, exerting a great influence over everything else that happens in the game. Notice the role of the pawns here: White controls the knight’s square with the pawn on e4; Black has no pawn that can chase the knight away—and also no knight, and no light-squared bishop. As a result, the knight probably will be impossible for Black to dislodge without a sacrifice. White had to fight to create this position; for an account of the battle, see Weeramantry’s first-rate book Best Lessons of a Chess Coach.
The conditions of a good outpost square may seem numerous, but creating them is a suitable task to keep you busy when you aren’t playing a tactic. Some of them might take care of themselves; others require work. Realize, first, that every time you move a pawn forward you weaken the squares it used to protect. If the pawns on either side of a square have moved forward or are off the board, the square becomes a hole where the other player eventually can put his pieces, comfortable in the knowledge that no pawn will be able to chase them away. It is common for such holes to be created inadvertently as each side advances and exchanges pawns. (In the diagram here, Black allowed a hole to be created on d5 by moving his e-pawn to e5 and by allowing his c-pawn to be removed.) This is a critical consideration to bear in mind both offensively and defensively. From an offensive standpoint, realize that the most important consequence of an exchange of pawns (or of any sequence) sometimes can be to foul up your opponent's pawn structure and leave holes behind. On the defensive side, think carefully about whether your pawn moves or exchanges will result in holes that create outpost squares for your opponent’s knights and other pieces; place your pawns so that they guard (rather than occupy) the attractive squares where his knights might like to perch. A few pawns well-placed in this way can neutralize a knight quite thoroughly.
As for your opponent’s bishops, if one of them is off the board, then squares of the color the missing bishop used to patrol are natural candidates for outposts. Likewise, if you see a promising outpost square it is worth hunting down and exchanging away the enemy bishop that travels on squares of that color. If you then have to move a knight three times to get it onto a good outpost square, it may well be worth it. A knight often will not be a big factor in a game—and will not be able to make the types of moves seen in this chapter—unless it finds a suitable outpost; once it does find an outpost, it may dominate the rest of the action. Even if you cannot satisfy all of these criteria for an optimal outpost square, taking care of one or two of them—creating the characteristic pawn structure in particular—may create an outpost that is suitable for quite a while. (If you can’t get rid of the bishop on the color of the outpost square, for example, it may nevertheless be out of position to do anything about your knight.) And naturally a safe outpost may be easier to create later in the game when there are fewer enemy pieces on the board.