The knight endgame with pawns is strategically similar to the pawn endgame and all the varitions to look out for in pawn endgames apply. For a knight endgame you want to centralize your king in order to sheperd your pawns across to a queening square. You also want to centralize your knight, close to your king where it can be protected, so it may support or attack different spots on the board. Two things to remember are that if your opponent is down pawns they may attempt to sacrifice their knight to kill off your last pawns. They would do this because King and a knight vs a king is a draw. The second thing to remeber is the forking ability of the knight. One reason is that this is how you are going to pick off your opponents pawns by checking the king in a knight fork with one of your opponents pawns. Another reason is that to bring your pawn safely across the board you normally have keep your king right beside/in front of it (see The Opposition, King vs King and single pawn). If you queen your pawn and your King is on the 7th rank and diagonal to the new queen you have opened your self up for a fork, something your opponent will surely be looking for.

The knight and pawn endgame is essentially the player with the most pawns or a threatining passed pawn trying to queen his pawns and the losing (positionally) player trying to force a draw by killing off the pawn(s).

Endgames in Chess
Chess Openings