En passant (french for "in passing") and castling moves can sometimes confuse beginners.
En passant happens when a pawn moves two squares on its initial move, and on the very next turn of the other player, they can capture your pawn with one of their pawns on their 5th rank as if your pawn only moved one square. This sounds confusing so just see examples below.
After this I will discuss castling. Castling is the only way in chess to move two of your pieces at the same time in one turn. It helps to protect your king. Always castle with one hand, moving the king first. In real life chess tournaments playing with touch move rules, if you touch the rook first, you are unable to castle and instead are forced to only move the rook.
Notice that if a turn passes in the meantime you lose the opportunity to do en passant and capture your opponent's pawn as if it only moved 1 square.
Try en passant below. Assume your opponent just played b5.
Castling (on the kingside) is the move where you move your king two squares to the right (to g1/g8) and your king's rook to the other side (to f1/f8). Note the profile picture for this blog is an example of the white king castled on the kingside. Castling (on the queenside) is the move where you move your king two squares to the left (to c1/c8) and your rook goes on the other side (d1/d8). Note that you can only castle when there are no pieces between your king and rook on the first/eighth rank.
You lose the ability to castle on the kingside if you move your king's rook at all previously in the game. You lose the ability to castle on the queenside if you move your queen's rook at all previously in the game. You lose the ability to castle on either side for the remainder of the game if you move your king at all off his original square of e1/e8 even if you move the king back to its starting square.
Here is an example of castling on the kingside.
Here is an example of both players castling on the queenside
Note that there are two circumstances in which you may not castle on a particular turn, but may do so when the particular condition is no longer met. These conditions are that your king may not castle while he is in check and the king cannot castle "through check." Naturally also the king can never "move into check" when he is done castling. Here I'll also remind beginners that the white king and black king can never be exactly touching side-by-side one square from each other.
Example below of white being unable to castle because his king is in check (from black's queen on e4).
Example of black being unable to castle "through check"
Note the bishop on a3 is guarding the f8 square.
Strategically castling is beneficial in that it often gets your king to the side of the board, where he will often be safer. Castle in the following positions.
Note white can castle on either the kingside or queenside. Castle on the queenside.