Normally, you are given the example of a sky diver:
1) As soon as the parachutist jumps, only weight acts, so no drag and they are accelerating downwards at the acceleration of freefall (9.81ms2). Resultant force is not zero, and it is downwards.
2) Later in the jump, they are still accelerating downwards but at an acceleration less than 9.81ms2 as drag is acting now. Weight > Drag so they still move downwards with a resultant force which is also downwards.
3) When they first open the parachute, the large surface area increases the drag force enourmously, so they accelerate upwards, with drag > weight, and resultant force now upwards.
4) A while after opening the parachute, the drag = weight which means they are at terminal velocity as the net force is 0, because the 2 forces are equal and they are travelling at a constant speed in the downward direction.
So, terminal velocity occurs when the drag force is equal to the weight, when the net force is 0 (no acceleration, constant velocity).
Any questions, feel free to ask