Demolishing a concrete driveway, patio, or slab typically involves breaking it up, hauling away the debris, and grading the site. There are several tools that contractors use to break up and remove concrete. When most people think of concrete removal, they generally think of jackhammers, but Bobcats with hydraulic or pneumatic breaker attachments are extremely common.
The contractor will often bring a roll-off dumpster to the site, but don't assume; make sure you confirm this with them. Then, once the concrete is broken, they will load the debris into the dumpster with the Bobcat and then transport the dumpster and debris to the nearest landfill or recycling facility.