One thing that applies both strategically and tactically is material advantage. If you command more pieces, or more powerful pieces, than your opponent, you will have greater opportunity.
A knight is about as valuable as a bishop (these two are called minor pieces), but less valuable than a rook, and less still than a queen (rooks and queens are called major pieces).
Three pawns are likely to be more useful than a knight in the endgame, but in the middlegame a knight is often more powerful. Two minor pieces are stronger than a single rook. Two rooks are stronger than a queen, but not by much.
One commonly used simple scoring system is 1 point for a pawn, 3 for a knight or bishop, 5 for a rook, and 9 for a queen. Under a system like this, giving up a knight or bishop in order to win a rook ("winning the exchange") is advantageous and is worth about two pawns. This of course ignores such complications as the current position and freedom of the pieces involved, but it is a good starting point.
This guide is licensed under the GNU Free Documentation License. It uses material from the Wikipedia.