In the simplest case, the lines would have the same number of points. Say we have line A, which has 5 points, and line B, which also has 5 points. At the start of the sketch line A would be displayed and line B would not but its points are stored. When it's morphing time (ha ha, never get to say that validly in context), for every point of line A, a target location is a point of line B, and the points of line A are tweened until they are line B.

In Processing you probably would want to use curves or beziers instead of lines to make it look nice.