How would object fall under the force of gravity if there were no air resistance

Regardless of its weight, the object would accelerate downward at 9.8 meters per second. If a feather and a bowling ball are dropped together in a vacuum, they land at the same time.

With air resistance, the object would accelerate until it reached it's terminal velocity. This is the speed at which air resistance prevents the object from speeding up any more.

Without air resistance, the object would continue to accelerate until it was stopped by something (like the ground).

Interestingly, your question has a very real application. Satellites that orbit Earth are in space where there is (pretty much) no air resistance, and they are, in a sense, continually falling around our planet. (Please see the link I provided for more info about this)

I just want to make sure you get that it is an acceleration: 9.8 meters / second /second.
For each second it has gotten faster by another 9.8 factor.

it would fall at a rate of 9.8 meters per second because of the lack of air resistance.