Longer Arm
Make the swinging arm of the catapult longer to increase the firing range. This will cause a longer arc of travel before the object launches, and will let the object build up more speed. If this is a DIY catapult, make sure the arm is adjustable.
Crossbar Position
Experiment with the position of the crossbar. Raise it or lower it. The purpose of this is to change the angle at which the swinging arm releases the object. This will affect the firing range of the catapult. Adjust the position of the crossbar until you achieve the best firing range. Also try affixing pieces of wood between the crossbar and the swinging arm as another way of adjusting the firing angle.
Ammunition Choice
Finding the right ammunition for a catapult is about finding a balance. You need to balance the wind resistance of the object with density and weight. You want to have a small, dense object that won't get stopped by the resistance of the air. But if the object is too heavy, it will limit its own range. And, if you are trying to knock objects over, you will need the ammunition to be heavy enough to do this. Experiment with metal shot or stones of various sizes until you find ammunition that is most effective for your catapult.
Safety
Wear safety goggles while using your catapult. Never fire a catapult at people or animals. When testing a catapult for the first time, give yourself plenty of distance in front of the catapult. Don't fire the catapult at anything that might get damaged, like windows, garden plants or vehicles. Some might consider a catapult a weapon. Don't use a catapult where weapons of all kinds are illegal.