One method starts with a choice for the total energy , E.
Once E is selected, find a value of x for which V(x) = E. (call that value x0 )
Then since p = ± √2m sqrt( E - V(x)), a first point on the phase plot (p,x) is (0, x0)
Since the argument of the square root cannot be allowed to be negative, the next points the next x value must be
either to the left or right of x0 and there will be two corresponding p values (± something)
This process can be continued to get additional points.
Selecting different values of E will generate a family of trajectories.
Of course there might be more than one value of x for which V(x) = E. Generally the trajectories started from different
such points will join up. A good example of this is the simple harmonic oscillator.