Survey your asphalt. Walk the area that you wish to get rid of. On the outside of this area, use a small shovel to dig down to the end of the asphalt. This will give you an idea how thick the asphalt is and how much force will be required to dislodge it. The thicker it is, the tougher the work will be.
Demolish the asphalt. Depending on the device you use, this can take many hours or days. If you use a jackhammer, work slowly -- always moving backwards. Decide on small sections to break apart and focus only on that, not the entire area. If you use a backhoe, you will finish much quicker. Either way, you need to observe safety guidelines at all times.
Load the chunks into your wheelbarrow and take them to your truck. Load the truck until it is safely full. Do not add more weight than your truck can handle. Small jobs can be done with a pickup in two or three trips. Larger jobs may require you to rent a dump truck.
Find your local recycling center to properly dispose of your asphalt. Depending on where you live, the recycling center may pay you for your asphalt by the pound, or you may be required to pay them. To discover which applies to you, contact them before you set out.