It may often be useful to think about what your opponent would like to play if it was his move. If it is a good thing for your opponent to get something, it is a good thing for you to stop him from getting it. To stop him from playing on a point, you can play there yourself.
Note that your move need not always be exactly the same move as he would have played. Rather, it often is a move in the same general area. Still, one can often settle the issue of who gets a key point simply by occupying it yourself.
See for example: