The Burj Khalifa, also known as the Burj Dubai, was, following its completion, the tallest building in the world. As with most skyscraper constructions, cranes will usually play a massive role, being primarily used to lift up the beams used for the structure of the building, but also for most of the heavy materials which need to be lifted to their intended floor.
Working out how they were going to find a crane which was able to lift their load to 828m in height was, thankfully, unnecessary, as due to the architecture of the building, every time one spire was completed another platform for the cranes would become available, allowing the cranes to be moved up, where they could then help with the construction of the next level.
Most cranes aren’t able to be made that tall, not that it is impossible, only that the taller they get the less exact you’re able to be with them. This is why architects will often have to compensate their designs to allow for their use.