Now in the solution, I understand how the game tree has been constructed but that's about it. Once the game tree has been constructed I don't understand at all how we work backwards from the terminal vertices to arrive at the value of 0 for the game. Shouldn't the value of the game be 1 as then P1 would receive the max payoff from P2, but then I arrived at this answer just by looking at all the payoff values in which the value of 1 was the highest which is obviously not the right way to work out the value of the game. But otherwise once the game tree has been constructed I don't even know how to begin finding out the value of the game and don't understand how we work backwards from each of the terminal vertices.
Any help would be much appreciated.
Player $2$ minimises the payoff, and Player $1$ maximises it. Thus you can work backwards on the basis that each player will play accordingly. This yields the following payoffs:
\begin{array}{} -14&&0&&1&&-9&&0\\ &-14&&0&&-9&&-9\\ &&0&&0&&-9\\ &&&0&&-9\\ &&\hphantom{-9}&\hphantom{-9}&0 \end{array}
The green path in your diagram shows the optimal moves, with Player $2$ being indifferent between the two moves on her first turn that both yield a payoff of $0$.