If you find yourself accelerating in your car and sensing a vibration as you speed up, your tires may be imbalanced. It sounds like a minor issue, but if they aren't addressed, imbalanced tires can cause damage to your bearings, shocks and wheel assembly. Ideally, you should visit a mechanic or similar professional for help on the matter. They have the equipment to do the job properly. It's not a hugely difficult process, however, and if you have the right know-how, you can balance your own tires safely.
Jack your car up with a wheel jack and remove the lug nuts of the imbalanced tire with a lug wrench.
Detach the tire and wheel from the car and place it on a tire balancer by lowering the tire onto the balancer's central shaft through the wheel hub and securing it in place. It should spin gently in the balancer when you are done.
Give the tire a soft turn and release it, allowing it to spin in the balancer. The heavier side will be drawn down and the lighter side will be drawn up. Let the wheel stop spinning, with the light side closest to the ceiling. Mark that point with a piece of chalk.
Place wheel weights along the inside of the tire directly below the chalk mark. The weights should have an adhesive side that will allow you to do this easily.
Check to see that you've used the right amount of weights by turning the wheel until the weighted part stands at the 9 o'clock position. Then release the wheel. If it turns counterclockwise towards the floor, you need to reduce the number of weights you've used. If it turns clockwise towards the ceiling, you need to add more weights.
Adjust the number of weights until you can place the weighted part at the 9 o'clock position and have the tire remain motionless (turning neither up nor down).
Press a piece of duct tape over the weights to better secure them in place, then detach the tire from the balancer.
Place the tire back on the car, tighten the lug nuts, and lower the jack.
It's a good idea to remove any other wheel weights you may have on the tire before you begin. You can still balance the tire, but it's trickier if they are on. Since wheel weights come uniform sizes (typically .709gr.), you may need to "make your best guess" when balancing tires in this manner. The balance may not be perfect; just try to come as close as you can.
Take care when using the car jack and let someone nearby know what you are doing. If the jack slips, it could pin part of your body under the car.