Draw up a few columns like so:
Here is my scrappy copy - I'm sure yours will look much nicer, but at least I haven't psyched you out of the exercise by beautifully ruled lines etc!
One column is for things said about, or to, God.
The second column is for things said about other people (in this case, David's enemies).
The third column is for things David says about, or to, himself.
As you do this, you will see David looking in two directions and working out what he will do. You will find the background to Psalm 56 in 1 Samuel 21:10-22:5.
I'd love to learn your observations!