Your car is in transit and the last step is meeting the driver at the destination. Delivery runs much like pickup.
What happens at delivery
The driver contacts you about 24 hours ahead with a time. When you both arrive, you pay the driver the agreed amount unless payment was already arranged through the shipping company. They unload the car and inspect it again. Inspect it yourself, in daylight, and compare against the pickup bill of lading and your photos. Any new damage gets marked on the BOL before you sign. Once you have both signed, the driver returns your key and you are done.
If something goes wrong
Most deliveries go smoothly. If there is a problem, try to resolve it with the carrier first. If the two of you cannot, call your broker. Stepping in at this point is part of their job.
Conclusion
If you have questions about delivery, ask your broker ahead of time. A good one will make sure the handoff goes smoothly and will help if it does not. That is what you paid them for.