How do I solve acceleration word problems?

Acceleration just means that you add the amount of acceleration to the object's current velocity.

So if something is moving at 5m/s^2, at one second it would be moving 5m/s, then at two it would be 25m/s, then at three 125m/s, etc.

I haven't been in physics for almost a year, so I may be incorrect. But that's what I remember.