The first number in 1. e4 Nc6, the "1.", is the move number. In this case, the first move of the game for white, e4, followed by blacks response, Nc6.
An upper case letter signifies the piece that is being moved. B for Bishop, N for Knight, K for King, Q for Queen, R for Rook. Pawns do not get the designation "P", and instead the piece letter is left out.
So, in the original example the notation means: On the first move (1.) white moved pawn to e4 (e4) and black responded by moving the Knight to the c6 square (Nc6)
The notation: O-O or O-O-O, means that the King has castled, where O-O is kingside castling, and O-O-O is queenside.
Some other things to note are "x" "+", where an x signifies a piece taking another piece like Nxd4 means Knight takes on the d4 square.
whereas a + is designated to a move that checks the King, and a "#" is checkmate.
The very last thing to note is that when two pieces can move to the square you'll see notation like 9. Rhf1, which just means that both Rooks can move to the f1 square, and the rook on the H file will move to f1(or R1f4, if both Rooks are on the F file it designates the Rook on the first rank move up to the fourth).