Tactic versus strategy
A strategy is a long plan, the whole game in miniature. A tactic is short and sharp: a small sequence of moves that wins material or forces the opponent's pieces onto bad squares. Most quick wins in chess come from tactics, not strategy. If you can learn to spot one of the patterns below, you will be grabbing free pieces for a long time.
The fork
A fork is one piece attacking two or more of your opponent's pieces at the same time. Because a player only gets one move per turn, your opponent can answer only one of those threats. Whichever piece they leave, you take.
The knight is famous for forks, because it attacks eight squares at once and moves in a way that is easy to overlook. Picture a knight aimed at both an enemy rook and an enemy bishop. The defender saves one, and you win the other. That trade, forced by a single piece, is the whole idea of a fork. A queen can fork across an entire board, and even a pawn can do it in the right spot.
The pin
A pin is a piece that cannot safely move, because leaving its square would expose something more valuable behind it. Usually what hides behind is the king. Pinned pieces are frozen in place, which makes them easy targets.
Pins are the work of long-range pieces: rooks, bishops, and queens. A rook lines up with an enemy knight that stands between it and the enemy king. The knight could technically move, but any move would open the line to the king, which is illegal. That knight is effectively dead weight. The pin is a beautiful, quiet way to take a piece off the board without ever touching it.
The skewer
A skewer is like a pin, but the order is reversed. The more valuable piece stands in front of a less valuable one, both on the same line. When the valuable front piece runs away from an attack, it opens the line, and the piece behind is lost as well.
Only queens, rooks, and bishops can make a skewer, because only they travel in straight lines. The classic version is a queen standing between your bishop and your king. Either the queen retreats and the bishop is lost, or she stays and the king is in danger. You win either way.
Counting exchanges
Before you trade pieces, count. How many of your pieces attack the square in question, and how many of your opponent's defend it? Then put a value on what you are about to swap, using the standard material values: pawn 1, knight and bishop 3, rook 5, queen 9. The king has no number, because losing the game matters more than any trade.
Beginners lose material in exchanges because they stop counting. You might trade pieces that look equal, only to realize an unconsidered defender was sitting behind the square. So the simplest tactic of all is arithmetic: count before you capture, and never trade a rook for a pawn to save a single turn.
Forks, pins, and skewers all share one trait. Each one asks your opponent to give up something they do not want to give up. Learn to see those moments, and you will start winning pieces without fighting for them.