|Photo credit: Petr Novák, Wikipedia|
First, the symbols for the pieces:
Okay, so let's say your queen took the pawn about to be promoted on the d7 square. It would look like this: Qxd7. The "Q" at the beginning means Queen, the letter "x" in the middle means the Queen just took something, and finally, d7 is the square.
Tips: In chess notation the piece symbol always goes first [unless it's a pawn, because they don't have a symbol.] Also, if there is a capture, the x would go after the symbol. Finally, if a check or a checkmate, the + or # always goes last.
So, if white plays "Knight takes e3 check," then that would look like this: Nxe3+. Or, if Bishop moves to b4, you would say Bb4. Castling is trickier. Castling on the kingside of the board [the side that the king is on] looks like this: O-O. Castling queenside looks like this: O-O-O. These rules are the basic rules of chess notation, and if you need help, feel free to ask in the comments.