There are two ways of doing it. The first way is to put your wheels on a machine and let it run. It will show how much weight or something like that to put to balance your tyre. The second way is by jacking up your car and accelerate while another guy will be sitting near the wheel to "feel" the vibration. Then, he'ss use the weight to see if it's balanced or not. This will be done till he is satisfied that the wheel is not vibrating any more. This explanation is based on what I see. Why, how and the terms I used may not be correct.
Anyway, just send it to another shop to do it. Very cheap only.