This game does have a number of theorems known about it, but re-deriving tough theory is not necessary for the problem as stated. The key idea for solving a question like this with a program is the concept of winning positions and losing positions (sometimes called $N$-positions and $P$-positions).
For example, $(7,7)$ is a winning position since if the pawn is at $(7,7)$ the next player to move can win by moving the pawn south-west by $7$ units (the OP said "by any number of fields"). More interestingly, $(1,2)$ is a losing position since the next player can only move to $(0,2)$, $(1,1)$, $(1,0)$, or $(0,1)$, all of which are definitely winning positions since the next player from any of them can end the game immediately. Therefore, $(1,3)$ is a winning position since moving to $(1,2)$ would be a good move.
The general definition is that a position is losing if all available moves are to winning positions ($(0,0)$ counts as losing since there are no available moves), and a position is winning if there is at least one move to a losing position. With this recursive definition, you can use a computer program (or pen and paper) to find all of the winning and losing positions among $(a,b)$ for $0\le a,b\le24$. It might be useful to arrange your results in a table or matrix.
It will turn out that the losing positions have a vague pattern, and that all positions of the form $(24,b)$ for $0\le b\le24$ are winning positions, so the "second player" can win no matter which of those positions the "first player" places the pawn. The winning first moves from each position like $(24,b)$ will then be clear from a table of the winning positions and losing positions: just make a move south, west, or south-west that leads to a losing position.
This problem can be done without a computer if you understand how to mark positions in your table by looking at it (it was first solved over 100 years ago), but to do so for larger numbers without the theorems that have been proven would require basically making a big table of winning and losing positions by hand and then seeing a pattern, making a very nonobvious guess at that pattern, then doing a lot of work to prove that pattern. This is why I asked about the context of the problem, because if you had just covered (in the book or class) a theorem which tells you a formula for the winning and losing positions already, then this becomes much easier.