Pawns move vertically one square at a time.
They can only move up the board, meaning for white they should always be moving up in numbers (2-3, 3-4, 4-5), and for black, they should always be moving down.
The only time a pawn can move more than one square is on its first move, where the pawn can move from the 2nd or 7th rank to the 4th or 5th rank respectively.
This wasn’t always a rule in chess, but it was used to speed up the game after players realised they were starting every game with two consecutive pawn moves.
Pawns capture diagonally. So, if a white pawn is on e4 and a black pawn is on d5, they can both capture each other.
On the other hand, if a white pawn is on e4 and a black pawn is on e5, those pawns will never capture each other and will remain in that position until a piece comes to a diagonal so that one can capture.
When a pawn reaches the other side of the board, it can be upgraded to any piece (although it’s usually a queen).
High-level chess players are always considering this fact because it is rare for players to give away any material at a high level.
Many grandmaster games have ended when one side is able to queen and the other is not.