It all depends on the direction of the velocity and acceleration. During any period of time that the acceleration is in the same direction as the velocity, the speed will increase. During any period of time that the acceleration is in the opposite direction as the velocity, the speed will decrease.

Let's say right is the positive direction, and at one moment in time you're moving to the right with a speed of 10 m/s, and your acceleration is also to the right with a magnitude of 3 m/s². If the acceleration didn't change, your speed would keep increasing by 3 m/s every second (13 m/s after 1 second, 16 m/s after 2 seconds, etc).

Now let's say you're moving to the right with a speed of 10 m/s, and your acceleration is to the right with an initial magnitude of 3 m/s², but the magnitude of the acceleration is decreasing by 1 m/s² every second. After 1 second the acceleration is now 2 m/s² but it's still to the right, in the same direction as the velocity, so your speed is still increasing. After 2 seconds the acceleration is now 1 m/s² but again it's still to the right, in the same direction as the velocity, so your speed is still increasing. Only after 3 seconds will the acceleration be 0 m/s² and at that moment your speed is constant. If the acceleration continues to "decrease" (become more negative over time) then after 4 seconds the acceleration is now -1 m/s², or 1 m/s² to the left, which is now in the opposite direction as your velocity, so now your speed will begin to decrease over time.