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In chess you basically want to maximize your "options". Aka, the number of squares your pieces control. Then, you will be able to see interesting combinations of moves you can make. Sacrifices, pins, checks, these combinations arise almost at a statistical random from the board.
The key is to make good, solid strategic moves to produce these eventualities.
For example:
-- In the early game it's extremely valued to get your pieces off your home rank and out into the fight. Sometimes chess teachers even instruct their students never to move the same piece twice in the opening.
-- Generally control of the center is very highly valued, as pieces placed in the center scope more of the board. **caveat: putting heavy-pieces like the rook and queen there early on is not a good idea as they are easily threatened and shoed-away
-- It's always beneficial to have your rook on a file (column) with less pawns. Particularly an open-file
-- A knight placed in the enemy half of the board which cannot be easily attacked or traded is sometimes called a "monster knight". Such a well placed knight is worth easily 5-7 pawns, rather than the usual 3.
-- Castling is an extremely valuable move and should almost always be done in a game. It gets the king into safety without wasting 5 moves doing it.
-- After castling, the pawns in front of the king should not be launched. You can move a pawn forward one step to provide an escape square against back-rank mating. But in general, launching those pawns forward creates so many weaknesses that moving them is a terrible idea long term.
As for the value of the pieces?
The bishops are more powerful in the late game. Especially the bishop-pair, which is worth more than the sum of its parts. Bishops in general are just a little bit more valuable than knights. The knights thrive more in closed positions and tactical positions.
It's generally recognized that 2 rooks is better than 1 queen, although it's harder to play. Commonly people will trade the queen for 2 rooks.
Pawns increase in value the further up the board they get. A pawn that's one square away from queening is worth like 5 pawns on the 2nd rank. "Connected passed pawns" are particularly valuable. This is 2 or more pawns that can defend each other, that don't have a pawn that can stop them or attack them.