The standard rule is that the bottom side moves first.
Most of the times, like in this case, it is black to move and win.
Otherwise it would be specified explicitly - like "white to move".
"You just have to move 23-19 and the game is over."
You probably meant the 10-14 move. If it is more convinient for you to use the chess notation then please do so, you will find both numeric and alphanumeric notations on the Board Numbers page to help you visualize the moves.
But jumping ahead - no, 10-14 is only a draw, it is never that simple.