Turning points have a derivative equal to zero and inflexion points have an extra condition where the second derivative is zero.
So you need to find out where the first derivative is zero and then test whether the second derivative at that point is also zero. If it's not zero (i.e the second derivative) then you have a normal turning point.
To understand this intuitively, the second derivative tells how the first derivative is changing: if its positive it means the slope is increasing and if its negative it means the slope is decreasing. At a turning point something "turns around" so it means the slope will continue to "decrease" or "increase" but if it's zero it means that it's not going to continue to "turn" as it has been up to the turning point and if this is the case, it's a point of inflexion (another name is called a saddle point).