@cathater
The board is divided into 8 rows (1-8) and 8 columns (a-h). White is always at the bottom (a1 is on white's left and h8 on black's). So, Qd3 means move the queen to the 4th column from (white's) left to (white's) row 3.
If black moves Qa6, it means move his queen to the rightmost column (ie white's 1st column=black's 8th column) and (white's) 6th row (=black's 3rd row)
NxP indeed means knight takes pawn. Sometimes you need to be more precise, so you mention which knight or which pawn.
The notation is:
R = Rook
K = King
B = Bishop
N= Knight
Q = Queen
If no piece is mentioned, it means the pawn.
See if you can replicate the following on a board from the start of a game.
1. e4 e5 (In a move of 2 plies (or a move by each opponent), white is mentioned first - sometimes you see 7. ... g5, this means white has made his move and black has moved his pawn to g5).
2. Nf3 Nc6
3. d4 exd4 (this means black's e pawn takes white's d pawn - this is an interesting opening full of traps)
If all this is beyond you, buy or borrow a chess for beginners book.
Regards