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I somewhat understand the concept of attacking the king and pieces, but "attacking" squares is a bit of a vague concept for me.

What are weak and strong squares? When do you use them? How do you create them?

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A square becomes weak when a pawn cannot protect it. For example, after white plays e2-e4 followed by c2-c4, the square on d4 becomes weak for white. Yet, the square on d4 becomes weak only when black has at least one piece that can use this weakness. In this example, the square on d4 is best used by a knight or bishop. To create a weakness, you should force your opponent to move a pawn forward. Make sure you have at least one piece that can take advantage of the created weak squares.

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Weak squares are squares which cannot be defended by a pawn. [1][2]

... that all of the squares behind the pawns are weak by default.

Counter-intuitively: Strong squares are squares which are defended by a pawns.

These square are very powerful places for opponents Knights or Bishops. No pawn can attack to these pieces. In below position, square d6 is a weak square for black and also strong square for its opponent.

1r1q2k1/1pbr2pp/2pNp3/p1P1Pp2/PP1P4/3R1QP1/6KP/1R6 w - - 0 1

or square f5, h4 and e6 are some weak squares for black and also f3 and d4 for white (however it's too late for black to put his Knight there)

1n3q2/p6p/1p1p1pk1/3PpN1p/4P3/1PQ3P1/P4P2/6K1 w - - 0 1

They're useful to place a Knight or Bishop in near the heart of opponents position. Usually making a weak square in the opponents land needs long term strategy. You have to force the opponent to pass its pawns...

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A weak square is a square that can no longer be protected by one of your pawns, or more generally, a square that can no longer easily be protected by one of your pieces.

enter image description here

In this example, the highlighted d5 square is weak for Black because they will never be able to control it with one of their pawns (this is actually a familiar sicilian pawn structure)

The concepts of weak squares are useful even to World Champions. In the following position, Botvinnik managed to exploit his opponent's weak squares in a few moves only: enter image description here

I describe how in this explanatory video about weak squares: https://youtu.be/AZG4PU_ejK0

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