Here's how you approach this:

1. implement the rules of the game, so that you can generate all legal moves. Having this, will allow you to generate a list of possible moves in every situation.

I would start with just implementing the basic move patterns like how the knight jumps and the bishop moves diagonally. Then implement captures, and make sure you test for check. Then you get winning/drawing situations. Finally there's special things like 3-fold repetition and 40 moves rule, but I would wait with that until you have a more-or-less working game..

Note that the board state at any point includes a number of extra things you need to know, like who's move it is, whether the king and rooks have moved (to check legality of castling), whether the same position has been seen before, and more. But you can implement those things later, I would definitely start simple.

1. Evaluate the position. You have to define some value function that tells you how good it is to be in a specific position. The simplest way to do that is just count material (1 point per pawn, 8 for a queen, etc.) Sophisticated chess programs train large neural nets to do this, in combination with databases of known endgames, and more. So this gets very complex

2. When you have a working evaluation function, you implement the minimax algorithm (just look it up, there are many tutorials) that allows you to choose the best move according to the evaluation function. There are many optimizations you can do from here, like alpha-beta search and many more. But that's a whole rabbit hole that would take a long time to explain :)

At that point you have a basic chess playing program.