To modify the path, you can edit the curve itself or translate the object constrained to the path.
For more information on editing curves in general, see Curves [Surface and Curve Modeling].
To modify a curve or trajectory
Move, add, or remove points on the curve as you would to edit any curve.
Translate the constrained object and use its new location to simultaneously create a new knot and keyframe on the path.
To do this, translate the object at the appropriate frame, then choose Create 
Path Save Key on Path or Save Locked Key on Path.
