The following picture is a representative 3Dimensional view of the electric potential (Volts) for a separated+ and - charge (an electric dipole).  The potential is represented by height (vertical) at positions in the xy plane.  The charges are located in the xy plane.  The positive at x=+1 y=0 and the negative at x=-1, y=0.   

Ideally the peaks should go to + and - infinity respectively, but I did not calculate the potential exactly at the charge (calculations are at points on a 150x150 grid....thats 22,500 points so be impressed).  This has the effect of smoothing over the "true" infinite peak at the charges.  Everywhere else the electric potential is fairly well represented. 

The steepness of the electric potential hill at some x,y point is proportional to the electric field at that point.  The direction in which the hill is steepest indicates the direction of the electric field at that point.  A positive charge released at rest somewhere on this plot would start moving downhill.   As it picks up speed the positive charge may not move in the most downhill direction (it may pick up momentum and cut accross E field lines).  You have seen this type of effect:  Consider water (or yourself) going down a waterslide.  When you start you are at the bottom of the rounded trough.  If placed, at rest, in the slide at any point along the slide you will start moving down hill in the direction that is steepest.  As you pick up speed you may slip up a wall on a curve.  The field line is like a line down the slide at the bottom of the trough.  Water does not follow that line as it picks up speed.  It slips all over the place.  However, water placed at rest anywhere in the slide will START OUT following that line!