How does the direction of the change in velocity compared to the direction of the acceleration?

Actually, because acceleration is the derivative of velocity (or change of velocity at a certain point), the acceleration can be in a different direction than the velocity. If the velocity's magnitude is increasing away from zero, then the acceleration is in the same direction as velocity. If the velocity is getting closer and closer to zero (either from the negative or positive end of the number line) then the acceleration is in the opposite direction of velocity.
Think of it like a car. When you are slowing down to stop at a light, your velocity is still going forwards, but your acceleration is negative because it is decreasing the velocity. A negative acceleration is another way of saying that the acceleration is going in the opposite direction of the frame of reference.
If the car is speeding up, the velocity is forward, and the acceleration is in the same direction because the change of velocity is positive.
Hope this helped! :D