When you are playing a game you've never played before or when you are designing a new playing engine, a good, universal and natural starting point is to try to get as close as possible to your winning goal as if there wasn't going to be any other player acting on the game.
It makes your first strategical concepts easier to design, because it is often about finding shortest paths or solving a solitaire puzzle.
I think most children do that when learning a game. I do. I would like to see it applied as well in any basic discussion about understanding a game.
More generally, you might look at the game rules and ignore some part. First the part that tells "there is another player" as I said. Then some other part if needed, such as "there is some other player's stones on the board" or some spatial dimension, flattening the board. It's like Generalization or Constraint Relaxation suggested by Geoge Pólya in Mathematical Research or by Judea Pearl in Computer Search.
In Chess for instance, it makes you focus on quickly threatening your opponent's King while cutting its escape routes and other anti-check answers in one move. It's infinitely much better than playing randomly.
The next step is then to add some concern about your opponent's distance to her own goal. How is she close to her goal? How can you slow her down? How can you keep getting closer to your own goal at the same time? How can you prevent her from slowing you down? How can she prevent you from preventing her... ?