Compared to the other pieces, which move on straight lines, the knight's L-shaped move makes it tricky for beginners and novices to deal with. The knight is a master of surprise, and can hop in and out of the most unexpected locations. A knight in the centre of the board can reach any other square in four moves or less. Take a look at the board below:
On each square is the number of moves it would take the white knight to reach it. Strong players can tell at a glance how many moves it would take their knight to reach a particular square. It's always important to bear in mind which squares your knight can reach quickly, and which ones would take a longer manoeuvre, in case you need to redeploy in a hurry. Try setting up a board and finding the different routes a knight could take to reach nearby squares.
There are a few things you should take note of that make working out knight moves easier:
Becuase the knight has limited range, it likes to be positioned in the centre of the board. Compare the white and black knights on the board below. The crosses show where black's knight can move, and the spots show where white's knight can move.
The black knight has eight possible moves, while the white knight has only three. Furthermore, the black knight can move into all four quadrants of the board, while white's knight wuold take some time to reach the queenside or the top of the board.
Clearly, that makes the centre the best place to put a knight. A good square in the centre, where a knight can take up position without fear of being exchanged off or chased away by a pawn, is known as an outpost. Holes in the opponent's pawn structure make good outposts for your knights, and an outpost is all the better if it is protected by one of your own pawns. You should try to find good outposts for your knights, and deny them to your opponent. Here is an example of a knight outpost:
Black's knight has a good outpost on d4. Note that white does not have a similar outpost on d5, because black has moved a pawn to c6 to prevent a white knight from settling there.
A knight on a strong outpost can be a great inconvenience to the opponent, as the knight controls squares in their camp and makes it awkward for their pieces to move around. It can also help in an attack on the enemy king.
Because it can only move to a maximum of eight squares (and only two if it stands in a corner), the knight is sometimes vulnerable to being trapped if it runs out of squares. Here is a typical example:
Because a knight always moves to a square of the opposite colour to the one it stands on, there is a danger that a badly placed knight can be dominated by the enemy bishop that moves on that colour square. Here is an example to show what we mean:
Black has allowed his knight to become cut off behind enemy lines, and the white bishop is able to prevent it from escaping single handedly. When a knight is on the edge of the board, a bishop three squares away like this can cover every sqaure the knight can move to. There is nothing black can do to stop the white king from strolling over and capturing the knight.
There is an old saying in chess - Knights on the rim are dim. Knights on the edge of the board have fewer squares to move to, take longer to reach the other side of the board, and can even be trapped. This doesn't mean you should never move your knights to the edge - sometimes you need to move a knight via an edge square to get it where you need it to go - but you should aways think twice about leaving them there.
If you're ever stuck for a move and don't know what to do next, try looking at the position of your knights. If you can manoeuvre them to a better square in the middle of the board, or to a nice hole near the enemy king, then that could be your plan. Planning in chess doesn't have to be a grand strategy leading all the way to eventual checkmate. Just setting short term goals like improving the position of a knight is often the right way to go.